Peel and wash the potatoes and carrots and cut into very small cubes. Peel onions and garlic, dice finely. Heat the oil in a large pan with a lid or a casserole dish. Fry the minced meat in it until crumbly.
Season with salt and pepper. Add onions and garlic, fry briefly. Stir in potatoes, carrots and 100 ml water. Cover and cook for 8-10 minutes. Let the mince cool down a little.
Let the dough rest for about 10 minutes at room temperature. Mix 3 eggs and sour cream and stir into the mince. Season with salt and pepper.
Grease a springform pan (26 cm Ø). Preheat the oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Melt butter. Place 4 pastry sheets overlapping in the mould so that the base and edge of the mould are covered.
Brush the individual leaves with liquid butter. Add the chopped mass. Place any protruding dough on top of the mince. Cut 3 dough sheets into 10 pieces each. Use the rest of the dough sheets for other purposes.
Fold the corners of each piece of dough into a small bag and screw in lightly. Press lightly into the mince with the tip facing upwards.
Bake in a hot oven for about 30 minutes. After about 5 minutes, slide a baking tray over the minced cake so that the tops of the dough do not burn. Whisk the egg yolks and 1 tbsp. milk. After about 25 minutes baking time, carefully brush the tops of the dough with the egg yolk.
Do not cover with the tray and finish baking.