Transactions with Related Parties (Details) $ in Thousands		3 Months Ended
	Apr. 30, 2019	Apr. 03, 2022 USD ($) yr Rate shares	Apr. 04, 2021 USD ($)	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	Mar. 29, 2020 restaurant
Related Party Transaction [Line Items]
Preferred stock, shares issued | shares		100						100
Board of directors, number of members		2
Franchise agreement, term		20 years
Accounts payable to BKC		$ 16,900						$ 16,300
Convertible Preferred Stock, Common Shares Issuable upon Conversion (in shares) | shares		9,414,580
Area Development Agreement, Prepaid Franchise Fees											$ 600
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		$ 400
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%
Initial Franchise Fees		$ 50
Property leases		224	230
Royalty Expense		$ 17,700	$ 17,100
Advertising Expense		15,600	$ 15,100
Operating lease cost		$ 6,700
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		95	100
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	10