Heat the oven to 350°F. Heat the butter and oil in a 9- or 10-inch nonstick skillet with an ovenproof handle (or cover a wooden or plastic handle with a thick layer of foil) over medium heat. Add the potatoes and onion and sauté for 20 to 25 min., stirring frequently, until the onions are softened and the potatoes are crispy on the surface and tender inside. Season with the thyme, 1/4 tsp. salt, and a pinch of pepper. Set aside. (You can make the filling up to this point a day in advance and refrigerate it. Bring it to room temperature before continuing.)
Combine the eggs, parsley, and the remaining salt and pepper in a medium mixing bowl; whisk until well blended. Stir in 1-1/4 cups of the Gruyère.
Flatten the potato filling in the skillet with a spatula and pour the egg mixture over. Cook over medium-low heat, occasionally stirring gently, until the bottom is lightly set and cooked, about 7 minutes. Arrange the tomatoes around the edge of the frittata. Sprinkle with the remaining 1/4 cup cheese. Put the skillet in the oven. Bake until the frittata is puffed and brown, about 12 minutes. Serve hot, warm, or at room temperature.
To get the frittata out of the pan, carefully run a flat wooden spatula around the edge.
Set a serving plate under the pan. Use the spatula to support the frittata as you tip the pan and pull it away.