This is especially true the higher the production volume / economies of scale. Imagine a burger joint where a worker pushes out a measley dozen burgers in an hour (I'd be surprised if volumes for most places are this low, but let's imagine). So, 5 min per burger.
At fed minimum wage of $7.25/hr, labor costs for those burgers are about 60 cents. A cheap burger is $2 right now, $3-$5 is much more typical. So even at output volumes as low as a dozen per hour, non-labor costs are a much greater portion of each of these burgers, like 70%-90%.
Double that minimum wage to $15/hr and assume all the cost is passed onto consumers and the price of these dozen burgers goes up by 65 cents. OK, let's assume a complete separation of cooking and register/order duties that requires at least two workers per dozen burgers per hour. We might see an increase of $2 per burger.
And since most people can't eat a dozen burgers an hour (much less the likely much higher output of burgers), a doubling of minimum wage far outpaces whatever price increase is passed on.
This is a simple model but even if you get more complicated, the outcome isn't much different. Generally speaking, even at economies of scale as low as a dozen per hour, wage increases outpace necessary price increases.
Where do wage increases contribute to dramatically increased costs? Lower volume high focus work where skilled labor is most of the cost of producing the product, but generally markets have long since decided these people get paid much more than minimum wage, so minimum wage increases have no effect here.
There's also the case where each unit requires a large team of labor. This tends to be at least semi-skilled in construction / fabrication / manufacturing where labor demands have long since left a legal wage floor behind.
The real question is why the misconception that minimum wage increases result in broad upward price spirals is so common when you can figure out why that's unlikely with math most people have learned by the time they're teenagers.
(I do think there's a good argument that labor markets are so thoroughly regional that it's probably better to have legal wage floors be set at the state and county level, but there's no reason a federal law couldn't be indexed off of local indicators with local guidance.)