Mix yeast and water. In a large bowl, beat together flour, yeast mixture, salt, sugar, olive oil, and lukewarm milk with a hand mixer until a smooth dough forms.
Grease a bowl with some oil and place the dough in the bowl. Cover with kitchen towel and let rest in a warm place for approx. 45 min. Knead the dough once, cover, and let rest for approx. 15 min. more.
Meanwhile, grate Gouda cheese and mozzarella, and crumble feta cheese. Beat an egg in a bowl and whisk in the cheese.
Pre-heat oven to 230°C/450°F. Dust work surface with some flour. Place the dough onto the surface and divide the dough into small pieces of equal size. Use your hand to knead the dough pieces into a round shape. Then fold in the edges to form an oval shape. Place the dough onto a parchment-lined baking sheet. Distribute the cheese mixture evenly onto the dough. Bake for approx. 15 min.
Remove from oven. Use two spoons to create a hollow in the middle of each piece of bread. Crack an egg in each hollow and return to oven. Bake for approx. 5 min. or until egg white is set but yolk is still runny. Serve with a sprinkle of Maldon sea salt and dill. Enjoy!