Most languages have one standard way of making declarative sentences, like "we eat a sandwich". English is weird in that we have three different ways to make declarative sentences : "we eat a sandwich", "we are eating a sandwich", "we do eat a sandwich". It's one of the things that confuses everyone learning English hehe.
I think boterham is a specific meal, like a slice of buttered bread. "We eat bread" is more "we eat this foodstuff in general" (and would translate as wij eten brood), while "we eat a slice of bread" sounds like you're recalling a specific serving. Think of saying "I drink beer" (general action) vs. "I drink a beer" (specific instance).
Food and drink can get strange as far as using mass nouns vs. countable nouns.
eten is plural (used when the subject is we or they) eet is singular (for example I eat or she eats)