Related Parties (Details) $ in Thousands		3 Months Ended		12 Months Ended
	Apr. 30, 2019 USD ($) state	Jan. 02, 2022 USD ($) Rate shares	Apr. 04, 2021 USD ($)	Jan. 02, 2022 USD ($) yr Rate shares	Jan. 03, 2021 USD ($) shares	Dec. 29, 2019 USD ($) restaurant shares	Sep. 30, 2025 restaurant	Sep. 30, 2024 restaurant	Sep. 30, 2023 restaurant	Sep. 30, 2022 restaurant	Sep. 30, 2021 restaurant	Jan. 04, 2021 state restaurant	Dec. 31, 2017
Related Party Transaction [Line Items]
Preferred Stock, Shares Issued | shares		100		100	100
Franchise Term | yr				20
Board of directors, number of members		2		2
Franchise Agreement, Term				20 years
Related Party Transaction, Accounts Payable		$ 31,164		$ 31,164	$ 27,596
Franchise Agreement, Number Of States | state	16
Franchise Agreement, Number Of Additional States | state	4
Franchise Agreement, Remodeling Expense	$ 3,000
Settlement, Approval of Restaurant Development			$ 1,900
Monthly Digital Platform Fee		$ 1,300
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant											4	50
Area Development Agreement, Percentage Of New Restaurants To Be In Kentucky, Tennessee And Indiana												80.00%
Area Development Agreement, Number Of Restaurants To Be Acquired | restaurant												500
Area Development Agreement, Number Of States | state												16
Area Development Agreement, Prepaid Franchise Fees						$ 600
Lessee, Operating Leases, Rent Expense, Net				$ 122,662	118,444	107,147
Scenario, Forecast | Subsequent Event
Related Party Transaction [Line Items]
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant							12	12	12	10
Related Party, Burger King Corporate [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Royalty Fee Rate | Rate		4.50%		4.50%
Royalty Expense				$ 72,800	67,200	62,000
Related Party Transaction, Advertising Fee Rate | Rate		4.00%		4.00%
Advertising Expense				$ 64,000	$ 59,300	56,700
Leases, Number of Leased Restaurants		225		225	232								248
Related Party Transaction, Accounts Payable		$ 16,300		$ 16,300	$ 14,700
Related Party Transaction, Percentage of Voting Interests Acquired | Rate		15.50%		15.50%
Lessee, Operating Leases, Rent Expense, Net				$ 26,900	$ 25,900	$ 27,400
Affiliated Entity [Member]
Related Party Transaction [Line Items]
Franchise Fees, Initial, Net				$ 50
Popeyes Franchises [Member]
Related Party Transaction [Line Items]
Right Of First Refusal, Number Of Franchises | restaurant						80
Right of First Refusal, Term	6 years
Property Leases Identical to BKC's Lease with Third Party [Member] | Affiliated Entity [Member]
Related Party Transaction [Line Items]
Leases, Number of Leased Restaurants		96		96
Series B Preferred Stock [Member]
Related Party Transaction [Line Items]
Preferred Stock, Shares Issued | shares		100		100
Popeyes Franchises [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Royalty Fee Rate | Rate		5.00%		5.00%
Right of First Refusal, Number of States | shares						2