Transactions with Related Parties (Details)		3 Months Ended		9 Months Ended
	Apr. 30, 2019	Oct. 02, 2022 USD ($) restaurant Rate shares	Oct. 03, 2021 USD ($) restaurant	Oct. 02, 2022 USD ($) restaurant yr Rate shares	Oct. 03, 2021 USD ($) restaurant	Sep. 30, 2025 restaurant	Sep. 30, 2024 restaurant	Sep. 30, 2023 restaurant	Sep. 30, 2022 restaurant	Jan. 02, 2022 USD ($) shares	Sep. 30, 2021 restaurant	Jan. 04, 2021 state restaurant	Jan. 03, 2021 USD ($) shares	Sep. 27, 2020 restaurant
Related Party Transaction [Line Items]
Preferred stock, shares issued | shares		100		100						100
Board of directors, number of members		2		2
Franchise agreement, term				20 years
Accounts payable to BKC		$ 17,300,000		$ 17,300,000						$ 16,300,000
Convertible Preferred Stock, Common Shares Issuable upon Conversion (in shares) | shares		9,414,580		9,414,580
Area Development Agreement, Prepaid Franchise Fees													$ 600,000
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant									10		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
Monthly Digital Platform Fee		$ 600,000	$ 400,000	$ 1,500,000	$ 800,000
Franchise Term | yr				20
Popeyes Franchises
Related Party Transaction [Line Items]
Right of First Refusal, Number of States | shares													2
Affiliated Entity [Member]
Related Party Transaction [Line Items]
Preferred stock, ownership percentage if converted | Rate		15.00%		15.00%
Initial Franchise Fees				$ 50,000
Property leases | restaurant		221	226	221	226
Royalty Expense		$ 19,700,000	$ 18,600,000	$ 57,000,000	$ 54,400,000
Advertising Expense		17,400,000	16,300,000	50,300,000	47,900,000
Operating lease cost		$ 6,900,000	$ 6,700,000	$ 20,400,000	$ 20,200,000
Popeyes Franchises
Related Party Transaction [Line Items]
Right of first refusal, number of franchises | restaurant														80
Right of First Refusal, Term	6 years
BKC Subleases with third-party lessor [Member] | Affiliated Entity [Member]
Related Party Transaction [Line Items]
Property leases | restaurant		95	97	95	97
Burger King Corporate [Member] | Affiliated Entity [Member]
Related Party Transaction [Line Items]
Additional advertising funds		$ 120,000,000
Advertising fund contributions, additional funding, basis points		0.0050
Royalty Agreement Terms [Member] | Burger King Corporate [Member]
Related Party Transaction [Line Items]
Related party transaction, rate | Rate				4.50%
Royalty Agreement Terms [Member] | Popeyes [Member]
Related Party Transaction [Line Items]
Related party transaction, rate | Rate				5.00%
Selling and Marketing Expense [Member] | Affiliated Entity [Member]
Related Party Transaction [Line Items]
Related party transaction, rate | Rate		4.00%
Forecast [Member] | Subsequent Event [Member]
Related Party Transaction [Line Items]
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant						12	12	12