Warm the milk lukewarm. Mix milk, sugar and yeast. Cover and let rest for about 25 minutes. Mix flour and 1/2 tsp. salt in a bowl. Add yeast milk, 1 tbsp. oil, yoghurt and egg, knead to a smooth, supple dough.
Cover the dough and leave to rise in a warm place for about 1 hour.
Wash, clean and quarter the green tomatoes and remove the seeds. Wash basil, shake dry and pluck leaves from the stalks. Grate 50 g cheese finely. Coarsely chop nuts and roast them in a pan without fat for about 2 minutes.
Finely puree green tomatoes, basil, grated cheese and nuts with a hand blender. Let 4 tablespoons of oil run in drop by drop, season with salt and pepper.
Knead dough briefly and form into 5-7 balls of the same size. Leave to rest briefly. Roll out to thin oval-shaped flat cakes on a floured work surface. Heat up a large coated grill pan. Bake the flat cakes in it one after the other from each side for about 2 minutes.
Wash and halve the cherry tomatoes. Chop the rest of the cheese into fine shavings. Arrange naan breads, spread with pesto, add tomatoes and sprinkle with cheese.