Activate the Yeast: In a bowl, mix the dry yeast and sugar with the lukewarm water. Cover with a dry towel and let it sit for 10 minutes or until frothy.
Make the Dough: Add the flour, salt, and olive oil into the yeast mixture. Knead the dough by hand or using a stand mixer with a dough hook until it becomes smooth and elastic. Once done, place the dough in an oiled bowl, cover it, and let it rise in a warm spot for about 40 minutes.
Prepare the Oven: While the dough is rising, place a baking stone on the middle rack of your oven and preheat it to 250°C (480°F).
Shape the Pide: Divide the dough into four equal portions. Roll each portion into an oval about 25 cm (10 inches) long on parchment paper.
Add Cheese Edge and Shape: Place small pieces of mozzarella along the border of each oval. Fold the edges inward to seal in the cheese, forming a rim. Pinch the ends to create a traditional boat shape.
Add Toppings: Spread a thin layer of tomato sauce inside each boat. Sprinkle a mix of grated mozzarella, cheddar, and blue cheese on top. Crack an egg into the center of each pide.
Finish and Bake: Brush the edges of the crust with beaten egg and sprinkle with sesame seeds. Bake for approximately 12 minutes or until golden.
Serve: Once baked, sprinkle with fresh basil leaves, slice, and enjoy!