For the short pastry, put flour, 2 eggs, 1 teaspoon salt, 1 teaspoon sugar, 4 tablespoons cold water and butter in flakes in a mixing bowl. Knead first with the dough hooks of the hand mixer, then with your hands to a smooth dough.
Wrap in foil and chill for about 30 minutes.
For the filling, peel and finely dice the carrots. Peel, wash and chop the potatoes. Clean, wash and chop the peppers. Peel and finely dice onion and garlic.
Heat the oil in a frying pan. Fry the minced meat for approx. 10 minutes, turning it over until it is crumbly. After about 5 minutes add the prepared vegetables. Season with salt and pepper. Add the tomatoes, chop with a spatula, season with 1 teaspoon sugar, bring to the boil and simmer for about 10 minutes.
Let it cool down. Cut the feta into cubes.
Roll out half of the dough on a floured work surface until round (approx. 30 cm Ø). Place on a baking tray lined with baking paper. Mix the chopped mass and feta and spread approx. 3/4 of the chopped mass as an outer ring on the dough circle, leaving a distance of approx. 3 cm to the edge of the dough.
Pour the rest of the minced meat into the middle of the dough circle, leaving a gap of approx. 3 cm. Separate 1 egg. Spread the edge and the space between the dough with egg white. Roll out the other half of the dough round (approx. 32 cm Ø).
Place on the chopping circle. Press the outer edge. Press the dough in the middle with an upside down bowl (approx. 10 cm Ø).
Press in the edge with a fork. Cut the outer edge at 5-7 cm intervals. Turn the dough pieces one after the other by approx. 90° so that the filling faces upwards. Whisk the egg yolk and 1 tbsp. water. Spread the dough with it.
Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) on the lower rack for approx. 50 minutes. Serve with tzatziki and tomato salsa.