Khobz el Dar (Algerian Semolina Bread)

Mix 1/2 cup plus 2 tablespoons semolina, 2 tablespoons sesame seeds, sugar, yeast, and salt together in a large bowl. Whisk in oil, egg, and egg white. Stir in warm milk slowly until a liquid dough forms. Cover the bowl with a plate or plastic wrap; let stand at room temperature until frothy, about 1 hour. Stir in 2 3/4 cups flour with a wooden spoon until a sticky dough forms. Cover again and allow to rest for 30 minutes. Line a baking sheet with parchment paper or a baking mat. Sprinkle 1 tablespoon flour over the dough and your hands. Mix dough, adding flour as needed, 1 tablespoon at a time, until it pulls away from the sides of the bowl. Shape into a round loaf and place on the prepared baking sheet. Cover loosely with a towel and let rise for 1 hour in a warm place until loaf doubles in volume. Preheat oven to 400 degrees F (200 degrees C). Beat egg yolk and water in a bowl with a fork; brush over the entire surface of the loaf. Sprinkle 1 tablespoon sesame seeds on top. Bake in the preheated oven until loaf is golden brown, about 20 to 25 minutes.