Can you have your cake and eat it too?

The saying is, "...have your cake," not "...halve your cake," so the answer is no.

A bottle of wine may be a more useful metaphor, because you cannot have your wine (have meaning keep, save, possess, retain) and drink it too. Once a bottle is opened, the wine touches the air and it starts to change--you must choose (hence the saying): possess the thing--retain it--or consume it and have it be gone.

A single bullet might be the best metaphor. The cartridge can be spent or it can be retained...but it cannot be both. The very meaning of the saying is intended to portray that sense--of the difficult choice between committing something to use, or retaining that something for future use.

Yes, one could halve a cake and eat it too...but that's something else entirely.