Wash broccoli, divide into segments. Grate cheese. Sift flour, grind with butter, and a pinch of salt until crumbly. Add egg, ice water, and knead quickly but thoroughly. Roll out the dough, put it in a mold, prick with a fork.
In a bowl, combine half the cheese, yogurt, milk, eggs. Season, stir until smooth. Put broccoli and tomatoes in a mold with prepared crust, pour in the egg-milk mixture, and bake at 180 degrees for 30 minutes. Remove the pie, sprinkle with the remaining cheese and Provencal herbs, bake for another 10 minutes.