Cook pasta in boiling salted water according to package instructions. Drain, drain and put aside. Peel onion and garlic and chop finely. Wash basil, shake dry. Pluck off leaves and chop finely, except for something to garnish
Heat the oil in a pan and fry the minced meat until crumbly. Add onion and garlic and fry briefly. Season with salt and pepper. Add tomato paste and sauté briefly. Add 100 ml water, simmer for about 5 minutes. Season everything once again. Mix in pasta and basil. Coarsely grate both cheeses
Melt butter for the béchamel. Dust with flour and sauté while stirring. Gradually add milk and stock while stirring. Simmer for 5 minutes over a mild heat. Season to taste with salt, pepper and nutmeg
Form 4 nests from the pasta on a fat pan of the oven. Pour béchamel sauce evenly over them and sprinkle cheese over them. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 15 minutes. Remove from the oven. Slide the eggs individually into a cup first, then into the middle of the nests. Bake in the hot oven for another 10-15 minutes. Place the pasta nests on 4 plates and serve garnished with basil