Peel and chop the onion. Heat the oil. Sauté onion in it. Deglaze with strained tomatoes and tomato paste. Reduce for about 5 minutes. Season with salt, pepper and sugar. Cut ham into pieces.
Dice the cheese. Clean the mushrooms and cut them into small pieces. Heat the fat. Sauté the mushrooms for about 5 minutes. Season with salt and pepper. Roast toast slices until golden brown. Spread with tomato sauce.
Add mushrooms, ham, cheese and basil. Place the toasts on a baking tray and bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C / gas: level 3) for approx. 10 minutes.