Wash the potatoes thoroughly, grate them dry and cut or slice them into thin slices. Blanch in boiling salted water for about 1 minute. Drain, rinse with cold water and let drain. Clean and wash spring onions and cut into fine rings.
Stir cream cheese and milk until smooth. Season to taste with salt and pepper.
Unroll the tarte flambée dough, remove from the paper and cut in half crosswise on a floured work surface. Lightly fold in the corners of each half. Roll each half of the dough with a dough roller to an oval flat cake.
Spread each with half of the cream cheese cream, sprinkle with about half of the spring onions. Place about half of the potato slices on top in a fan shape. Season with salt and pepper. Line a baking tray (36 x 41 cm) with baking paper.
Place the tarte flambée on top of each other, drizzle with oil and bake in a preheated oven (electric cooker: 250 °C/ convection oven: 225 °C/ gas: see manufacturer) for approx. 15 minutes until crispy.
Wash the basil, shake dry and pluck the leaves. Take the tarte flambée out of the oven. Cover with ham and basil and cut into pieces.