Goodwill and Other Intangible Assets, net - Schedule of Other Intangible Assets (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Oct. 01, 2023	Oct. 02, 2022	Oct. 01, 2023	Oct. 02, 2022	Jan. 01, 2023
Intangible assets with definite lives
Gross Carrying Amount	$ 435,604		$ 435,604		$ 435,134
Accumulated Amortization	(144,084)		(144,084)		(126,946)
Net Amount	291,520		291,520		308,188
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Gross Carrying Amount	1,093,547		1,093,547		1,093,034
Accumulated Amortization	(144,084)		(144,084)		(126,946)
Net Amount	949,463		949,463		966,088
Amortization of intangible assets	7,400	$ 7,100	22,000	$ 21,300
Trade names and trademarks
Intangible assets with indefinite lives
Trade names and trademarks	657,943		657,943		657,900
Franchise agreements
Intangible assets with definite lives
Gross Carrying Amount	30,389		30,389		30,632
Accumulated Amortization	(10,382)		(10,382)		(9,372)
Net Amount	20,007		20,007		21,260
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	(10,382)		(10,382)		(9,372)
Customer relationships
Intangible assets with definite lives
Gross Carrying Amount	15,000		15,000		15,000
Accumulated Amortization	(6,197)		(6,197)		(5,548)
Net Amount	8,803		8,803		9,452
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	(6,197)		(6,197)		(5,548)
Reacquired franchise rights (1)
Intangible assets with definite lives
Gross Carrying Amount	390,215		390,215		383,002
Accumulated Amortization	(127,505)		(127,505)		(105,526)
Net Amount	262,710		262,710		277,476
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	(127,505)		(127,505)		(105,526)
Website development costs
Intangible assets with definite lives
Gross Carrying Amount	0		0		6,500
Accumulated Amortization	0		0		(6,500)
Net Amount	0		0		0
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	$ 0		$ 0		$ (6,500)