Heat 2/5 cup (100 ml) of the milk in a bowl, add 1 tablespoon of sugar to it and dissolve the yeast in this. Leave for about 10 minutes in a warm place to bubble.
Meanwhile, sift the flour, make a well in the middle of it and put the melted butter, sugar, honey, eggs, vinegar and salt in it. Begin to knead by hand, gradually add the yeast, while alternating with the remaining milk until you get a homogeneous dough.
Cover it with a damp cloth and leave in a warm place for about an hour to rise and double in volume. Knead the risen dough again and divide it into two equal parts. Remove the peaches from the compote, cut them into crescents, drain and place them on paper towels to dry.
Take one half of the dough and roll it out into a round crust with the diameter of the tray in which you will be baking it in. I used a 11 3/4″ (30 cm) tray.
Brush the tray with a little oil and place the rolled out crust in it. Roll out the other half of the dough into a round 3/4″ (2 cm) thick crust and using a small ring or glass, cut circles out of it. Arrange the ready circles on top of the dough in the tray, alternating them with pieces of peach, slightly overlapping them.
Beat the egg yolk and brush the pita with it. Leave it for 30 minutes to rise again and bake in a 338°F (170 °C) oven for about an hour until you get a golden color.
Finally, sprinkle it with powdered sugar if you like.