The most Instagram worthy dish there ever was!

1 1/3 cups all purpose flour (plus more for dusting)
2 teaspoons Kosher salt
3/4 teaspoon active dry yeast
1/2 teaspoon granulated sugar
1 tablespoon canola oil (plus more for greasing bowl)
1/3 cup milk (warmed)
1/3 cup water (warmed)
3 cups low-moisture mozzarella cheese (shredded)
1 1/4 cups feta cheese (crumbled)
1/4 cup Parmigiano-Reggiano (grated)
2 large egg yolks (room temperature, divided)
2 tablespoons unsalted butter (room temperature, divided)
Kosher salt and freshly ground black pepper (for tasting)

For the Dough: Preheat oven to 450ºF.
In the bowl of a stand mixer fitted with a dough hook, add flour, salt, yeast and sugar and mix on low speed. Add canola oil, milk and water and continue to mix on low until dough forms. Increase the speed to medium and knead for 2-3 minutes, until smooth and elastic. Remove the dough to a bowl greased with olive oil. Cover with plastic wrap and allow to rise until doubled in size, about 1 hour.
Remove the dough from the bowl to a floured surface and divide in half. Stretch one piece of dough into an oval shape about ½-inch thick. Cover the second piece of dough with a damp towel. Carefully place one oval onto the back of a lightly floured baking sheet. Place 1 cup of the cheese filling in the center then bring the long ends of the dough together and pinch to seal–the cheese is encased in the dough. Flip the filled dough over so the seam is on the bottom, and using a knife, make a 6-inch long cut into the center. Roll the edges of the slit dough toward the center under the cheese to create a cheese-filled crust with a well in the middle. Place another cup of cheese filling into the well, creating a mound of cheese. Sprinkle the boat with 2 tablespoons of grated Parmigiano-Reggiano. Pinch and twist the ends of the dough. Repeat this process with remaining dough and cheese filling. Bake for 12-15 minutes. Remove from the oven, place one egg yolk and 1 tablespoon of butter on top of the cheesy center. Serve immediately!
For the Cheese Filling: In a medium bowl, combine mozzarella and feta. Season with salt and pepper. Set aside.