I'm not a vegan or something, but my stomach can't take many chicken eggs in food.

I've got a recipe for a Imeritian khachapuri variant (cheese-filled flat bread) recipe where eggs are used as a "glue" (I think) for the filling. (Sorry, the recipe itself is in Russian, I'll give any details if needed.)

Now, this recipe also uses eggs for the dough. That is a bit too much eggs for me. I'd like to replace eggs in filling with something.

Note that I'm not interested in commercial (or "chemical") solutions.

Update:

Ingrediends for the filling:

• Soft cheese (150 g)
• Hard cheese (150 g)
• Two eggs
• Some herbs and salt to taste

Here is a Google Translate version of the recipe. I think it is more or less understandable.