Sartre believed that it was impossible to abdicate the responsibility of making choices, because to choose to do nothing is still a choice -- in other words, "nothing" is a kind of something. So one might humorously imagine that Sartre would also think that "no cream" is a kind of something that could be different from "no milk."

Excellent! I once went to a local burger place - they have a menu full of the various types of burgers, all loaded with everything. My kids are super picky, so I asked for a burger, with nothing except the burger and the bun.

Server looked confused - but which burger did I want? It became apparent that while I could ask for a preset item and ask for removals, I could not actually go fully off menu. So I had to ask for "the cheese burger, without the cheese" (as somehow distinct to say, the bacon burger, without the bacon). I laughed at the ludicrousness of that, but now I see they were channeling Sartre! In retrospect it would have been a truly beautiful absurdity if see had come back and said "sorry, we have no cheese, do you want no bacon?"

Like the scene from Five Easy Pieces with Jack Nicholson. He asked the waitress for an omelet with a side of toast. She says they don't have a side of toast, so he asks for a chicken salad sandwich, on toasted wheat bread, and hold the mayonnaise, the lettuce and the chicken salad.

I get the feeling that it's also easier for the cashier to put it into the point of sale / ordering system. There are buttons for specific menu items, and then buttons to remove things from them, but no buttons to build a burger from scratch.

I remember working at the drive thru for Wendy’s. I learned all about some clever orders that saved you $0.50-2.00 by ordering things a certain way. I can’t remember anything specific, but I remember one time asking, “so you want an X?” And they came back with “no, put it in exactly how I told you.”

In the ice cream situation, broken and down mean the same thing. In the Sartre anecdote, milk and cream mean the same thing.

No, it was a logic error on the part of the server. Since he requested without cream, their lack of cream was irrelevant.