In a large mixing bowl, stir together the flour, sugar, salt, and instant yeast with a whisk. Pour in the olive oil and the lukewarm milk, then mix with a spatula. Slowly add the water while stirring until a sticky, lumpy dough forms. The dough will be wet, so a spatula keeps it easier to combine.

Oil a second large bowl with a little olive oil and slide the sticky dough into it. Flip the dough to coat all sides. Cover the bowl with a clean kitchen towel and let it rise in a warm spot until doubled in volume, about 40-60 minutes depending on room temperature.

Scatter a light layer of flour on a work surface and dump the risen dough onto it. Using floured hands, fold the outer edges toward the center, without kneading. Gather it into a smooth-ish ball and divide it into two equal pieces.

Line a baking sheet with parchment paper and dust it with flour. Set an oven-safe pan or bowl of water on the bottom oven rack, then preheat the oven to 425°F (220°C).

Place one piece of dough on the prepared pan and press it outward with your fingertips into a round about 1/2 inch (1.27 cm) thick. If it springs back, wait a few minutes and try again, or lightly wet your hands to help press.

Moisten your fingertips and press a circle into the dough, about 1/2 inch (1.27 cm) from the edge, to outline the border. Then press horizontal and vertical lines inside that circle to form a diamond pattern. Shape the second dough ball the same way, leaving space between them on the sheet.

Cover the shaped breads with a towel or plastic wrap and let them rest for a second proof, 20-30 minutes.

Whisk the egg yolk and yogurt together in a small bowl. Brush this mixture over the entire surface of both breads; you may have a little left over.

Press the indentations down once more with your fingers to sharpen the pattern. Sprinkle sesame seeds evenly over the top.

Bake the breads on the lowest rack for 13-15 minutes, until the tops are golden brown and the bottoms no longer look doughy. Rotate the pan halfway through if one side is browning faster.

Pull the pan from the oven and cover the breads with a clean kitchen towel for 10 minutes. This steams the crust slightly to keep the crumb soft. Move the breads to a cooling rack after that rest.

Serve warm for the best fluffy texture, or cool completely and serve at room temperature with soups, kebabs, hummus, or a meze spread.