Preheat the oven to 450 degrees F. Line 2 baking sheets with parchment paper. In a medium bowl, combine the mozzarella, feta, and provolone. Add 1 egg and mix well to combine. In a small bowl, massage the kale with 1 tablespoon olive oil and a pinch of salt and pepper. Divide the pizza dough in half. On a lightly floured surface, push/roll each dough out into a rough oval shape (about a 10 inches long). Transfer the dough to the prepared baking sheets. Spoon the cheese mixture evenly into the center of each dough, leaving a 1 inch border. Fold the edges over the cheese to enclose the cheese and form a "boat". Top each with kale. Transfer to the oven and bake for 10 minutes or until the crust is golden and the cheese is melting. Remove from the oven and crack an egg into the center of each Khachapuri (you can also just use the egg yolk). Return the Khachapuri to the oven and bake another 3-5 minutes, until the white is just barely set. Meanwhile, in a small bowl, combine the remaining olive oil, basil, parsley, dill, garlic, crushed red pepper, salt and pepper. Remove the Khachapuri and add 1 tablespoon butter to the center of each. Stir the butter and egg into the cheese, this will finish cooking the egg. Brush the herb sauce over the warm Khachapuri. Serve immediately and enjoy!