In a large mixing bowl, whisk together the flour, sugar, salt, and instant yeast. Add the olive oil and lukewarm milk, then mix with a spatula. Gradually pour in the water while stirring until a sticky dough forms. A spatula works best for this step as the dough is quite sticky.

Brush a separate large bowl with olive oil and transfer the dough into it. Cover with a clean kitchen towel and let it rest in a warm place until it doubles in size. This takes about 50-60 minutes in cooler weather or around 40 minutes on warmer days.

Once the dough has risen, lightly flour your work surface and transfer the dough onto it. Fold the edges toward the center without kneading. Shape into a ball and divide it into two equal pieces.

Line a baking sheet with parchment paper and sprinkle some flour on it. Place an oven-safe bowl filled with water at the bottom of the oven and preheat to 425°F (220°C).

Place one dough ball on the prepared baking sheet and gently spread it out using your hands to about ½ inch (1.27 cm) thickness, forming a round shape. If the dough sticks, wet your fingers slightly.

To create the traditional pide pattern, wet your fingertips and press firmly to make deep indentations. First, make a circular indentation about ½ inch (1.27 cm) from the edge. Then, create vertical and horizontal indentations inside the circle to form a diamond pattern. Repeat with the second dough ball.

In a small bowl, whisk together the egg yolk and yogurt, then spread this mixture over the prepared breads using a brush or your hands. You might not need to use all of it and let the breads rest for a second rise, about 20 minutes. Sprinkle sesame seeds on each.

Before baking, press down on the indentations again to reinforce the pattern. Place the baking sheet on the lowest rack of the oven and bake for 13-15 minutes, until the breads are golden on top and no longer pale at the bottom.

Remove from the oven and cover the breads with a clean kitchen towel for 10 minutes. Then, transfer them to a cooling rack or another kitchen towel to cool completely.

Serve warm for the best taste, or at room temperature.