Transactions with Related Parties (Details) $ in Thousands		3 Months Ended		9 Months Ended
	Apr. 30, 2019 USD ($) state	Oct. 03, 2021 USD ($) Rate shares	Sep. 27, 2020 USD ($)	Oct. 03, 2021 USD ($) yr Rate shares	Sep. 27, 2020 USD ($)	Sep. 30, 2025 restaurant	Sep. 30, 2024 restaurant	Sep. 30, 2023 restaurant	Sep. 30, 2022 restaurant	Sep. 30, 2021 restaurant	Jan. 04, 2021 state restaurant	Jan. 03, 2021 USD ($) shares	Dec. 29, 2019 USD ($) shares	Sep. 29, 2019 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		$ 15,100		$ 15,100								$ 14,700
Other Income		$ 1,053		$ 111	$ 1,432
Convertible Preferred Stock, Common Shares Issuable upon Conversion (in shares) | shares		9,414,580		9,414,580
Franchise Agreement, Number Of States | state	16
Franchise Agreement, Remodeling Expense	$ 3,000
Franchise Agreement, Number Of Additional States | state	4
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		$ 800
Franchise Term | yr				20
Due to Related Parties, Current, Accrued Dividends		$ 3,900		$ 3,900
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		15.50%		15.50%
Initial Franchise Fees				$ 50
Property leases		226		226
Operating Leases, Rent Expense		$ 6,700	$ 6,900	$ 20,200	19,900
Royalty Expense		18,600	17,800	54,400	48,800
Advertising Expense		$ 16,300	$ 15,600	$ 47,900	$ 43,200
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		97		97
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