Pour the flour onto a floured work surface and make a depression in the middle. Add the dough ingredients and knead everything into a smooth pasta dough. (Add 1/2 to one tablespoon of water if the dough is too dry). Wrap the noodle dough in foil and let it rest for 30 to 45 minutes.
In the meantime, wash the thyme for the filling, dab dry and remove the leaves. Peel the garlic and press it through a garlic press. Wash and peel the aubergines and cut them into very fine cubes.
Heat olive oil in a frying pan. Sauté the aubergine, garlic and thyme in it. Deglaze with stock, season with salt and pepper and braise until all liquid has evaporated. Let it cool down.
Crumble the goat's cheese and stir into the filling together with the egg yolk. For the sauce, also pluck the thyme leaves and put something aside for garnishing. Heat the butter in a pot and fry the thyme in it until the butter begins to brown.
Add cream and simmer the sauce for five to minutes. Stir in Parmesan cheese and season with salt and pepper. Set aside. Roll out the pasta dough very thinly (preferably with a pasta machine) and cut out 30 circles of ten centimetres in diameter.
Spread a teaspoonful of filling on each and brush the edges with egg white. Fold over to half moons and press the edges firmly. Cook for five minutes in plenty of boiling salted water.
In the meantime heat up the sauce. Pour the pasta pockets onto a sieve, rinse with cold water and spread on preheated plates. Pour the sauce over the pasta, sprinkle with thyme and garnish.