Preheat the oven to 400 degrees.
Bring a pot of water to boil.
Peel and chop the potatoes. Add the potatoes to the water and boil until tender.
While the potatoes are boiling, heat the olive oil in a large skillet. Cook the onion, carrot, and garlic in the olive oil until tender. Add ground beef and brown. Once browned, add tomato paste and herbs de Provence. Stir until thoroughly mixed. Salt and pepper to taste. Remove from heat. Stir in the grated Parmesan cheese.
Drain the potatoes and mash them. Stir in butter and sour cream. Salt and pepper to taste.
Add meat mixture to a 9 inch x 9 inch baking dish. Layer the mashed potatoes on top of the meat. Top with Gruyère cheese.
Bake until the cheese is melted.
Garnish with scallions and serve.