For the dough:
For the yeast dough, put the flour in a bowl. Make a well in the middle, crumble in the yeast and mix with 125 ml of lukewarm water and some flour from the edge. Cover bowl with a cloth. Leave the pre-dough to rise for about 20 minutes in a warm, draft-free place.
Add oil and salt to the pre-dough, knead vigorously and beat to form a smooth dough. Form a ball and leave covered for a another 45 minutes until doubled in volume.
For the asparagus topping:
Cut off the bottom of the asparagus spears and use a vegetable peeler to peel the spears from top to bottom. Start just below the head and peel thicker towards the bottom.
Preheat the oven to 485 F (250 C). Divide the yeast dough into 4 portions, roll each out into a 1 cm thick long flatbread and place on a baking tray lined with baking paper. Cover with a towel and let rise for 10 minutes.
Cut the asparagus into thirds and cook in boiling salted water for 5-6 minutes. Lift out with a sieve and drain well.
Mix the crème fraîche with a pinch of salt and a little pepper until smooth. Spread the crème fraîche on the flatbreads. Lay the asparagus spears on top and sprinkle the grated parmesan over them.
Bake the flatbreads in the oven for 10-15 minutes until crispy. Mix olive oil with parsley and season with salt and pepper. Take the tarte flambée out of the oven and drizzle with the herb oil. Place the ham slices on the hot tarte flambée and serve immediately.
