How does the false-conditional work in "I made sandwiches if you want some"?

It is elliptical: a main clause like [have some] or [please take some] has been left out.

I made sandwiches; [have some] if you want some.

It is akin to requests like these:

Please come with me; if you would be so kind [I would be much obliged].

Ladies and gentlemen; if you will come with me [I will be most thankful].

Somewhat similar is this construction:

She's different, [you will understand] if you know what I mean.

I'm not so sure that this construction is really best understood as ellipsis, at least not in quite as simple a manner as Cerberus suggests.

Rather, I would argue that the example sentence:

"I made sandwiches, if you want some."   (1)

should be understood as an instance of a more general construction:

"[statement of fact], if [the listener cares about the fact]"

where, functionally, the purpose of the second half is to avoid implying any presumptions that someone might otherwise read into the first half. Basically, it's a shorter way of saying "I made some sandwiches, but you don't have to take any just to be polite, and you certainly shouldn't assume that I thought you looked really hungry or anything."

As such, I believe the origin of this construction would be better understood as a generalization of similar (but more conventionally grammatical) expressions like:

"Here are some sandwiches, if you want some."   (2)

or even:

"You may take a sandwich, if you want some."   (3)

The conditional in sentence (3) is perfectly fine according to ordinary English grammar: if the listener wants a sandwich, they may take one. One could argue that it's still redundant, in the sense that the listener is presumably permitted to take a sandwich even if they don't really want one, but the conditional still serves a useful function in informing the listener that the preceding statement of permission doesn't (at least on the face of it) carry any implied obligation, and that they're free to ignore it if the conditional is false. Indeed, (3) could still further be seen as a polite rephrasing of:

"Take a sandwich, if you want some."   (4)

which some might find too brusque, even if the blunt imperative is softened by the conditional following it.

Thus, we may see (3) as a softer rephrasing of (4), sacrificing some grammatical precision for politeness, and (2) in turn as a yet more more polite form of (3), carefully avoiding any overt implication that the speaker might have any authority over the listener, such that they could grant or deny them permission. It could be seen as ellipsis of:

"Here are some sandwiches; [you may take some] if you want some."   (2*)

but I would argue that it could just as easily be interpreted as a direct analogue of (3), where the direct statement of permission is simply replaced by a statement of fact implying the permission.

In a sense, the conditional in all of (1), (2) and (3) may be understood as a meta-conditional, not qualifying the factual existence of sandwiches as such, but rather the assumption that the listener should care about what was just said. That is to say, I think (1) might be better expanded to:

"I made some sandwiches, [which might interest you] if you want some."   (1*)

somewhat analogously to, say:

"The sandwiches are over there, [which might interest you] if that's what you're looking for."

or even:

"I'll be in my office, [which you might want to know] if you need me."