Activate the Yeast: In a bowl, mix the dry yeast and sugar with the lukewarm water and cover with a dry towel. Let it sit for 10 minutes, or until frothy.
Make the Dough: Add the flour, salt, and olive oil, then knead the dough (either by hand or using a stand mixer with a dough hook) until smooth and elastic. Place the dough in an oiled bowl, cover with plastic wrap or a shower cap, and let rise in a warm place for about 40 minutes, or until doubled in size. (Tip: Use the proofing function of your oven, if available.)
Prepare the Oven: Place a baking stone in the middle rack of your oven and preheat it to 250°C (480°F). The baking stone ensures even heat distribution and helps create a crispy crust.
Shape the Pide: Divide the dough into four equal portions and shape each into a ball. Roll each ball into an oval about 25 cm (10 inches) long on parchment paper.
Add Cheese Edge and Shape: Place small mozzarella pieces 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 with a mix of grated mozzarella, cheddar, and blue cheese. Crack an egg into the center of each pide.
Finish and Bake: Brush the crust edges with beaten egg and sprinkle with sesame seeds. Using a pizza peel or the back of a tray, slide each pide (on its parchment) onto the hot baking stone. Bake for 12 minutes, or until the crust is golden and the egg is cooked to your liking.
While one pide is baking, prepare the next one.
After baking, sprinkle with fresh basil leaves, slice, and enjoy!