Transactions with Related Parties (Details) $ in Thousands		1 Months Ended	2 Months Ended	3 Months Ended		6 Months Ended
	Jul. 02, 2023 USD ($) Rate shares	May 31, 2023 USD ($)	Jan. 01, 2023 USD ($) restaurant shares	Jul. 02, 2023 USD ($) Rate shares	Jul. 03, 2022 USD ($)	Jul. 02, 2023 USD ($) yr Rate shares	Jul. 03, 2022 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
Related Party Transaction [Line Items]
Preferred stock, shares issued | shares	100		100	100		100
Convertible Preferred Stock, Common Shares Issuable upon Conversion (in shares) | shares	9,414,580			9,414,580		9,414,580
Board of directors, number of members	2			2		2
Franchise agreement, term						20 years
Franchise Term | yr						20
Monthly Digital Platform Fee				$ 700	$ 500	$ 1,400	$ 900
Other liabilities	$ 29,026		$ 25,687	29,026		29,026
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%
Restaurants completed | restaurant			6
Area Development Agreement, Number Of Restaurants To Be Acquired | restaurant													500
Area Development Agreement, Number Of States | state													16
Forecast [Member] | Subsequent Event
Related Party Transaction [Line Items]
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant								12	12	12
Burger King Corporate [Member]
Related Party Transaction [Line Items]
Technology Equipment, Right Of Use	1,200	$ 12,200
Repairs, Replacements, and Improvements Provided	$ 7,300			$ 7,300		$ 7,300
Burger King Corporate [Member] | Royalty Agreement Terms [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate						4.50%
Popeyes [Member] | Royalty Agreement Terms [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate						5.00%
Affiliated Entity [Member]
Related Party Transaction [Line Items]
Preferred stock, ownership percentage if converted | Rate	14.70%			14.70%		14.70%
Initial Franchise Fees						$ 50
Royalty Expense				$ 21,700	19,600	41,500	37,300
Advertising Expense				$ 19,200	$ 17,300	$ 36,400	$ 33,000
Property leases	218			218	222	218	222
Operating lease cost				$ 7,300	$ 6,800	$ 14,300	$ 13,500
Affiliated Entity [Member] | Selling and Marketing Expense [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Rate | Rate				4.00%
Affiliated Entity [Member] | Burger King Corporate [Member]
Related Party Transaction [Line Items]
Maximum borrowing capacity			$ 120,000
BKC
Related Party Transaction [Line Items]
Other liabilities	$ 20,000		16,000	$ 20,000		20,000
PLK
Related Party Transaction [Line Items]
Other liabilities	$ 20,000		$ 16,000	$ 20,000		$ 20,000
Related Party
Related Party Transaction [Line Items]
Property leases	96			96	95	96	95