In a mixing bowl, combine flour, yeast, and salt. Gradually add warm water and olive oil, mixing until a dough forms.

Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.

Place the dough in a lightly oiled bowl, cover, and let rise for 1 hour or until doubled in size.

Preheat the oven to 450°F (230°C).

Punch down the dough and divide it into four equal pieces. Roll each piece into a rough oval shape.

Mix mozzarella and feta cheese together. Spread a portion of the cheese mixture onto the middle of each dough oval.

Fold the edges of the dough towards the center, creating a boat shape with a well for the cheese in the middle.

Place the Khachapuri on a baking sheet and bake for about 10 minutes.

Remove from oven, crack an egg onto the cheese of each Khachapuri, and return to the oven for another 5-8 minutes, or until the eggs are cooked to your preference.

Remove from the oven and place a tablespoon of butter on top of each Khachapuri. Serve hot.