Tear the broccoli into small rosettes and blanch them for 4-5 min. in boiling and salted water. Strain immediately and rinse under cold running water.
Peel the potatoes, wash them and cut into pieces. Boil until semi-cooked in salted water.
Oil a large tray, mix the potatoes and broccoli, sprinkle with the spices to taste, a little olive oil and stir.
Pour on the cream (and milk if needed), shake the tray, arrange pieces of butter on top and put it to bake in a preheated 392°F (200 °C) oven. Bake until the veggies gain a light crisp.
Then distribute slices of cheese on top and return to the oven for 10-15 min. to finish baking.