Put the flour in a bowl. Crumble yeast into it. Add sugar, salt, oil and 150 ml lukewarm water. Knead to a smooth dough with the dough hooks of the hand mixer. Cover and leave to rise in a warm place for about 30 minutes.
Knead again, cut in half and roll out on a floured work surface to two round bottoms (approx. 20 cm Ø). Place on a baking tray lined with baking paper, brush with strained tomatoes and pre-bake in a preheated oven (electric cooker: 200 °C/ gas: level 3) for approx. 10 minutes.
In the meantime clean, wash and slice the mushrooms. Chop the ham. Grate cheese. Cover pizzas with mushrooms and ham. Season with pepper and thyme, sprinkle cheese on top. Bake for another 10-15 minutes.