Peel and finely dice the onion and garlic. Clean the mushrooms, possibly wash and halve them. Heat oil in a pot. Fry the mushrooms in it in 2 portions until golden brown. Fry onion and garlic briefly.
Add the tomato paste and sweat it in. Add tomatoes and juice and chop a little with a spatula. Season with salt, pepper and 1 pinch of sugar. Stir in herbs and simmer for about 15 minutes.
Cook the pasta in 3-4 l boiling salted water (approx. 1 teaspoon salt per litre) according to package instructions.
For the béchamel sauce, melt butter in a pot. Sprinkle with flour and sauté while stirring until light yellow. Stir in milk and 1⁄4 l water. Bring the sauce to the boil, stir in the stock and simmer for about 5 minutes, stirring occasionally.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Drain the pasta.
Drain the olives and artichokes. Quarter the artichoke hearts. Add both to the tomato sauce and simmer for about 5 minutes. Season the tomato and béchamel sauce with salt and pepper. Cut the rind off the Taleggio thinly.
Dice Taleggio and Mozzarella finely and mix.
Place the pasta alternately with the tomato, béchamel sauce and about half of the cheese in an ovenproof dish. Finally, sprinkle with the rest of the cheese. Bake in a hot oven for about 30 minutes until golden brown.