Boil the potatoes in a pan of lightly salted water for about 15 minutes.
Drain and let the potatoes cool.
While the potatoes are cooking, chop the onions, peel and dice the carrots.
Cut the tomatoes into small cubes.
Peel, peel and cut the garlic clove into 4.
Heat 1 tsp. olive oil in a very large skillet over medium-high heat.
Add the garlic and sauté for 1 minute, then add the ground meat. Cook for about 10 minutes, until the meat is cooked through and a little golden.
Remove the meat from the pan, place it on a plate.
In the same pan, add 1 tsp. olive oil. Saute the onions over medium heat for 3 minutes, until tender and lightly golden.
Add the diced tomatoes, sauté for 2 minutes.
Then add the carrots, peas, cooked meat, salt and pepper. Sauté for 2 minutes, stirring.
Finally add the broth and Provence herbs. Reduce heat to low and cook uncovered for about 20 minutes, stirring occasionally.
After 20 minutes, if the broth is still too runny, add a teaspoon of cornstarch to thicken.
While the meat is simmering, mash the potatoes with a fork, gradually adding the milk.
Melt the butter in the microwave and add it to the mash, stirring. Salt, pepper, and add the nutmeg.
Grate the cheese, add it to the puree, mixing well.
Preheat the oven to 190 ° C.
When the mash and the meat are ready, spread a generous layer of meat on the bottom of a baking dish.
Place the mash on top, packing well so that there is no air.
Drizzle with a light drizzle of olive oil, then bake for 30 minutes and Serve hot.