In a small bowl, dissolve yeast in warm water and let it stand until bubbly.
In a large bowl, combine flour with the yeast mixture and knead until a dough forms. Let it rest for 30 minutes.
Preheat the oven to 450°F (230°C).
Roll the dough into a rough oval shape on a floured surface.
Place the cheese blend onto the center of the dough, spreading it out evenly. Fold the edges of the dough over to create a boat shape.
Bake the khachapuri in the preheated oven for about 15 minutes until the crust is golden brown.
Remove from the oven, make a small well in the center of the cheese, and crack an egg into it.
Return to the oven and bake for an additional 5-7 minutes or until the egg is cooked to your liking.
Serve the khachapuri hot, breaking the egg yolk and mixing it with the cheese before eating.