Transactions with Related Parties (Details) $ in Thousands		1 Months Ended	2 Months Ended	3 Months Ended		9 Months Ended
	Jul. 02, 2023 USD ($)	May 31, 2023 USD ($)	Jan. 01, 2023 USD ($) restaurant shares	Oct. 01, 2023 USD ($) Rate shares	Oct. 02, 2022 USD ($)	Oct. 01, 2023 USD ($) yr Rate shares	Oct. 02, 2022 USD ($)	Sep. 30, 2025 restaurant	Sep. 30, 2024 restaurant	Sep. 30, 2023 restaurant	Sep. 30, 2022 restaurant	Sep. 30, 2021 restaurant	Jan. 04, 2021 restaurant state
Related Party Transaction [Line Items]
Preferred stock, shares issued | shares			100	100		100
Convertible Preferred Stock, Common Shares Issuable upon Conversion (in shares) | shares				9,414,580		9,414,580
Board of directors, number of members				2		2
Franchise agreement, term						20 years
Franchise Term | yr						20
Monthly Digital Platform Fee				$ 800	$ 600	$ 2,200	$ 1,500
Other liabilities			$ 25,687	37,946		37,946
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant										12	10	4	50
Area Development Agreement, Percentage Of New Restaurants To Be In Kentucky, Tennessee And Indiana													80.00%
Restaurants completed | restaurant			6
Area Development Agreement, Number Of Restaurants To Be Acquired | restaurant													500
Area Development Agreement, Number Of States | state													16
Forecast | Subsequent Event
Related Party Transaction [Line Items]
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant								12	12
Burger King Corporate
Related Party Transaction [Line Items]
Technology Equipment, Right Of Use	$ 3,400	$ 12,200
Repairs, Replacements, and Improvements Provided				$ 10,500		$ 10,500
Burger King Corporate | Royalty Agreement Terms
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate						4.50%
Popeyes | Royalty Agreement Terms
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate						5.00%
Affiliated Entity
Related Party Transaction [Line Items]
Preferred stock, ownership percentage if converted | Rate				14.70%		14.70%
Initial Franchise Fees						$ 50
Royalty Expense				$ 21,300	19,700	62,800	57,000
Advertising Expense				$ 18,800	$ 17,400	$ 55,200	$ 50,300
Property leases				218	221	218	221
Operating lease cost				$ 7,400	$ 6,900	$ 21,800	$ 20,400
Affiliated Entity | Selling and Marketing Expense
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate				4.00%
Affiliated Entity | Burger King Corporate
Related Party Transaction [Line Items]
Maximum borrowing capacity			$ 120,000
BKC
Related Party Transaction [Line Items]
Other liabilities			16,000	$ 20,500		20,500
PLK
Related Party Transaction [Line Items]
Other liabilities			$ 16,000	$ 20,500		$ 20,500
Related Party
Related Party Transaction [Line Items]
Property leases				96	95	96	95