Transactions with Related Parties (Details) $ in Thousands	1 Months Ended	2 Months Ended	3 Months Ended		12 Months Ended
	Dec. 31, 2023 USD ($) restaurant shares	Jan. 01, 2023 USD ($) restaurant	Mar. 31, 2024 USD ($) yr restaurant Rate shares	Apr. 02, 2023 USD ($)	Dec. 31, 2023 USD ($) restaurant shares	Sep. 30, 2025 restaurant	Sep. 30, 2024 restaurant	Sep. 30, 2023 restaurant	Sep. 30, 2022 restaurant	Sep. 30, 2021 restaurant	Jan. 04, 2021 restaurant state
Related Party Transaction [Line Items]
Preferred stock, shares issued | shares	100		100		100
Convertible Preferred Stock, Common Shares Issuable upon Conversion (in shares) | shares			9,414,580
Board of directors, number of members			2
Franchise agreement, term			20 years
Franchise Term | yr			20
Monthly Digital Platform Fee			$ 900	$ 700
Other liabilities	$ 29,120		$ 49,426		$ 29,120
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant								12	10	4	50
Area Development Agreement, Percentage Of New Restaurants To Be In Kentucky, Tennessee And Indiana											80.00%
Restaurants completed | restaurant	3	6			3
Area Development Agreement, Number Of Restaurants To Be Acquired | restaurant											500
Area Development Agreement, Number Of States | state											16
Number of restaurants | restaurant			227
Number of restaurants remodeled | restaurant			8
Related Party
Related Party Transaction [Line Items]
Purchase commitment	$ 1,700		$ 2,500
Purchase Commitment, Kiosks, Additional Funding	2,500		3,700
Purchase commitment, total	4,200		6,200
Additional Receivables			1,500
Contributions Received			400
Forecast [Member] | Subsequent Event
Related Party Transaction [Line Items]
Area Development Agreement, Restaurants To Be Opened, Built, And Operated | restaurant						12	12
Burger King Corporate [Member]
Related Party Transaction [Line Items]
Technology Equipment, Right Of Use			11,400		$ 12,200
Self-ordering kiosks			1,800
Repairs, Replacements, and Improvements Provided			$ 12,200
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			14.60%
Initial Franchise Fees			$ 50
Royalty Expense			20,300	19,800
Advertising Expense			$ 17,900	$ 17,400
Property leases			217	220
Operating lease cost			$ 7,300	$ 7,100
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	16,900		$ 17,900		16,900
PLK
Related Party Transaction [Line Items]
Other liabilities	$ 16,900		$ 17,900		$ 16,900
Related Party
Related Party Transaction [Line Items]
Property leases			95	93