Transactions with Related Parties (Details)		3 Months Ended		6 Months Ended
	Apr. 30, 2019	Jul. 03, 2022 USD ($) restaurant Rate shares	Jul. 04, 2021 USD ($) restaurant	Jul. 03, 2022 USD ($) restaurant yr Rate shares	Jul. 04, 2021 USD ($) restaurant	Sep. 30, 2025 restaurant	Sep. 30, 2024 restaurant	Sep. 30, 2023 restaurant	Sep. 30, 2022 restaurant	Jan. 02, 2022 USD ($) shares	Sep. 30, 2021 restaurant	Jan. 04, 2021 restaurant state	Jan. 03, 2021 USD ($) shares	Jun. 28, 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		$ 17,400,000		$ 17,400,000						$ 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											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		$ 500,000	$ 400,000	$ 900,000
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		222	227	222	227
Royalty Expense		$ 19,600,000	$ 18,700,000	$ 37,300,000	$ 35,800,000
Advertising Expense		17,300,000	$ 16,400,000	33,000,000	$ 31,500,000
Operating lease cost		$ 6,800,000		$ 13,500,000
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	98	95	98
Royalty Agreement Terms [Member] | Burger King Corporate [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate				4.50%
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	10