For the dough, knead 175 g flour, fat in flakes, 1/2 tsp salt and 4 tbsp cold water first with the dough hooks of the hand mixer, then with your hands to a smooth dough. Wrap in foil, chill for about 1 hour
Meanwhile wash the meat, dab dry and cut into cubes. Clean the leek, halve lengthwise, wash and cut into strips. Peel onion and garlic and chop finely. Clean, wash and halve the mushrooms. Wash thyme, dab dry, remove leaves from the stalks and chop finely, except for a little bit for sprinkling
Heat the oil in a pan, fry the meat well in it, remove. Sauté the mushrooms in the frying fat. Add onion, garlic, thyme and leek, fry briefly, dust with 2 tbsp. flour and sauté briefly. Add stock and cream while stirring. Add the meat and simmer for about 5 minutes. Season to taste with salt and pepper. Remove from the stove and let cool down
Grease a pie mould (approx. 24 cm Ø, 1 litre capacity). Whisk egg with milk. Roll out the dough on a floured work surface (approx. 25 cm Ø), except for a little bit for garnishing. Cut a hole in the middle (approx. 1.5 cm Ø). Fill chicken ragout into the form. Brush the edge of the mould with egg-milk. Carefully place the dough on top and press firmly all around with a fork
Roll out the remaining dough again. Cut out rings of different sizes (approx. 4-7.5 cm Ø). Spread on the dough and brush with egg-milk. Sprinkle with thyme. Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for approx. 25 minutes until golden brown. Remove from the oven, let cool for about 10 minutes and serve
Waiting time approx. 1 hour