This pillowy soft bread comes together quickly without any special equipment. It would work well with a variety of fillings, but the soft garlic cheese punched up with smoky chiles, fresh herbs and lemon is a bright combo against the buttery bread.
Stir the warm water and sugar together until dissolved, then stir in the yeast; set aside until foamy, about 5 minutes. Meanwhile, whisk the flour, baking powder and fine salt in a large bowl.
Add the butter to the flour mixture and work it in with your fingertips until the butter is in pea-size pieces. Make a well in the center of the flour mixture and add the yeast mixture and milk. Stir with a wooden spoon until the flour is completely moistened and the dough looks like a shaggy ball, switching to your hands and gently kneading to bring the dough together, if necessary. Cover the bowl and let the dough rise at room temperature until doubled in size, 1 to 1 1/2 hours.
When the dough is almost ready, make the filling: Combine the cheese, chiles, parsley, thyme and lemon zest in a small bowl. Mash and stir together with a small rubber spatula until smooth and spreadable. Set aside.
Turn out the dough onto a lightly floured surface and briefly knead until smooth, three or four times. Pat until about 1 inch thick, then fold into thirds like a letter and pat until 1 inch thick again. Rotate the dough 90 degrees and repeat folding and patting two more times. Divide into 2 equal pieces.
Lightly butter an upside-down rimmed baking sheet (or a rimless baking sheet). Roll out 1 piece of dough into an 11-inch round on a floured surface and transfer to the pan. Spread with the filling, stopping about 3/4 inch from the edge. Roll out the second piece of dough into an 11-inch round and place on top of the first. Pinch and press the edges of the dough together to seal.
Center the rim of a drinking glass (about 3 inches in diameter) in the middle of the dough; gently press to mark the center. At the 12 o’clock mark, cut through the dough with a very sharp knife from the glass to the edge, leaving the center circle uncut. Repeat at the 3 o’clock, 6 o’clock and 9 o’clock points on the circle to make 4 quarters. Halve each quarter to make 8 equal wedges; halve those to make 16 wedges.
Lift the edges of 2 wedges that are next to each other and twist them away from each other twice. Pinch the ends together to make a pointed tip. Repeat with the remaining pairs of wedges. Remove the glass and cover the dough with plastic wrap. Refrigerate until the filling is firm and the dough has puffed and risen slightly, 45 minutes to 1 hour.
Meanwhile, preheat the oven to 400˚ F. Uncover the dough and re-pinch any ends that came apart. Brush all over with the beaten egg and sprinkle with flaky salt. Bake until golden brown all over, especially around the center circle, 25 to 30 minutes. Let cool a few minutes on the baking sheet, then carefully slide onto a rack to cool completely. Serve at room temperature.