Revenue Recognition - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 02, 2024	Jan. 03, 2023	Dec. 28, 2021
Disaggregation of Revenue [Line Items]
Gift card liability, current	$ 2,222	$ 2,430
Revenue recognized for redemption of gift cards	2,800	3,400	$ 3,200
Gift card breakage	$ 300	500	300
Period in which initial fees received from franchisees will be recognized as revenue	20 years
Deferred revenue	$ 900	300
Initial fees from franchisees
Disaggregation of Revenue [Line Items]
Revenue recognized that was included in contract liability	200	100	$ 100
Accrued expenses and other current liabilities
Disaggregation of Revenue [Line Items]
Gift card liability, current	2,200	2,400
Other long-term liabilities
Disaggregation of Revenue [Line Items]
Gift card liability, non-current	$ 1,000	$ 700