Segment Information - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 29, 2025	Jun. 30, 2024	Jun. 29, 2025	Jun. 30, 2024
Disaggregation of Revenue [Line Items]
Total revenues	$ 529,166	$ 507,894	$ 1,047,475	$ 1,021,810
Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	178,989	184,640	352,870	375,891
Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	48,302	46,552	96,358	93,705
Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	234,576	214,322	463,517	431,834
Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	23,136	20,410	46,893	41,345
Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	44,163	41,970	87,837	79,035
Operating segments
Disaggregation of Revenue [Line Items]
Total revenues	524,243	503,704	1,035,337	1,015,901
Operating segments | Domestic Company-owned restaurants
Disaggregation of Revenue [Line Items]
Total revenues	175,797	173,207	346,592	349,431
Operating segments | Domestic Company-owned restaurants | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	175,797	173,207	346,592	349,431
Operating segments | Domestic Company-owned restaurants | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | Domestic Company-owned restaurants | Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | Domestic Company-owned restaurants | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | Domestic Company-owned restaurants | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America franchising
Disaggregation of Revenue [Line Items]
Total revenues	36,603	35,450	73,414	72,196
Operating segments | North America franchising | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America franchising | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	36,603	35,450	73,414	72,196
Operating segments | North America franchising | Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America franchising | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America franchising | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America commissaries
Disaggregation of Revenue [Line Items]
Total revenues	267,659	248,500	532,036	501,054
Operating segments | North America commissaries | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America commissaries | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America commissaries | Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	267,659	248,500	532,036	501,054
Operating segments | North America commissaries | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America commissaries | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | International
Disaggregation of Revenue [Line Items]
Total revenues	44,184	46,547	83,295	93,220
Operating segments | International | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	3,192	11,433	6,278	26,460
Operating segments | International | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	12,943	12,143	25,447	23,599
Operating segments | International | Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	19,730	16,125	35,752	30,350
Operating segments | International | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	3,409	3,787	6,693	6,852
Operating segments | International | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	4,910	3,059	9,125	5,959
All Other
Disaggregation of Revenue [Line Items]
Total revenues	73,761	69,312	148,092	134,519
All Other | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
All Other | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
All Other | Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
All Other | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	24,301	20,154	49,380	41,678
All Other | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	49,460	49,158	98,712	92,841
Elimination of Intersegment Revenue
Disaggregation of Revenue [Line Items]
Total revenues	(68,838)	(65,122)	(135,954)	(128,610)
Elimination of Intersegment Revenue | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Elimination of Intersegment Revenue | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	(1,244)	(1,041)	(2,503)	(2,090)
Elimination of Intersegment Revenue | Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	(52,813)	(50,303)	(104,271)	(99,570)
Elimination of Intersegment Revenue | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	(4,574)	(3,531)	(9,180)	(7,185)
Elimination of Intersegment Revenue | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	$ (10,207)	$ (10,247)	$ (20,000)	$ (19,765)