Warm the water to 35 F (35 C). Stir in the yeast and leave to rest for 5-6 minutes to activate it.
In a large mixing bowl, add 1 kilo of flour and make a well in the center. In the well, add the yeast water, sugar, salt, oil, milk, and one egg. Mix the ingredients from the middle of the bowl until a ball of dough forms. The dough should be soft and tacky, but not sticky. You may need to add more liquid depending on the humidity level (I needed a lot more in winter).
Cover the bowl and leave the dough to rise in a warm place for 2 hours. The dough will look spongy.
Preheat your oven to 475 F (246 C). Knead the dough and add a bit the remaining flour as necessary if the dough is sticky. Separate into 4 equal portions and leave to rest for 10 minutes.
In a small bowl, mix the shredded mozzarella and feta cheese with one egg. Set filling aside.
Shape each ball into a flat pointy oval (width of the baking sheet) on two flour-dusted baking sheets.
Spread a quarter of the cheese filling in an oval shape in the center of each boat. Keep it packed and smooth on top with a spoon.
Fold the sides of the dough in to create an edge and pinch the ends into points. Leave to rest for 10 min.
Bake for 12 minutes, or until lightly golden. Beat one egg in a small bowl for the wash.
Remove from the oven, brush the wash on the dough and crack an egg over the cheese on each boat.
Bake for 3 to 4 minutes, until the egg has just set but not fully cooked and the yolk is still runny.
Serve warm and topped with a generous pat of butter.