But what about open faced sandwiches? And cutting a burrito in half lengthwise (admittedly a dumb thing to do, but hey it's a thought experiment) would make it fit that definition of a sandwich as well. I do like where you're headed though, and I think we can definitely work with the idea that the way the bread is applied is important to what we consider a sandwich. I certainly think that it has to be a flat piece (or pieces) of bread on which the set of ingredients are applied. Your definition brings to light something I was playing around with as well: the idea that sandwiches are more defined on how they look than how they're actually made. Thus a sandwich could be anything that is surrounded by flat (or relatively flat) objects of the same general materials. However, this begs the question of what multidimensional sandwiches would look like (which is a super weird thing to thinks about).
The keyword is "between". If you cut a burrito in half, the ingredients wouldn't be contained between the two halves. They'd just be inside each half, without the other half being necessary. Open faced sandwiches are another thing entirely. They share more in common with toast than they do proper sandwiches. The crucial part of a sandwich is how it contains things. Open faced sandwiches don't contain, they support. They're the location that other things rest on. A sandwich, generally speaking (looking at you, hot dogs and some subs), should be able to be inverted. The issue here is that the word "sandwich" has two meanings. The first one, shit between bread (cgod), is the one I've been talking about. The second one is used like you were saying: things between other things. Ice cream sandwiches (cookies) are the best example I can think of. Notice though how when you hear the word "sandwich" by itself, you always think of the first use - a bread something. That might be the key right there.