In a large bowl, combine the flour and salt. Gradually add warm water and mix until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough back in the bowl, cover it with a towel, and let it rest for 30 minutes.
Preheat your oven to 450°F (230°C).
Divide the dough into 2 pieces and roll each into a rough oval shape.
Mix together Mozzarella and Feta cheese and place the mixture in the center of each piece of dough.
Fold the edges of the dough over the filling, creating a boat shape.
Transfer the khachapuri to a parchment-lined baking sheet and bake for 15-20 minutes until the bread is golden brown.
Remove from the oven and create a small well in the center of the cheese. Crack an egg into the well and return to the oven for 3-4 minutes, until the egg is set.
Serve warm and enjoy your delicious Khachapuri!