Crumble the yeast and mix with sugar until the yeast becomes liquid. Knead flour, 1/4 teaspoon salt, oil, 175 ml lukewarm water and yeast with the dough hooks of the hand mixer to a smooth dough.
Cover and leave to rise in a warm place for about 30 minutes. In the meantime peel onions and cut them into thin rings. Wash the thyme, shake dry and pluck the leaves, except for 4 stems. Knead yeast dough briefly and cut in half.
Roll out one half on a floured work surface to an oval flat cake (approx. 25 x 36 cm) and place it on a baking tray lined with baking paper. Spread the dough thinly with half of the cème fraîche and cover with half of the onion rings.
Season with salt and pepper, spread 100 g goat's cream cheese in pieces on top. Sprinkle half of the thyme leaves and twigs on top. Bake in the preheated oven (electric cooker: 250 °C/ convection oven: 225 °C/ gas: level 3) for 10-12 minutes.
Meanwhile roll out the second half of the dough in the same way, cover with the remaining ingredients and bake. Cut the tarte flambée into large pieces and serve warm.