Take mascarpone, milk, and eggs out of the refrigerator and set aside. Preheat oven to 425 degrees (F) and position rack near the bottom.

Place potato in a colander in the sink, toss with ¼ teaspoon each salt and pepper, and press down on them with your hands to remove most excess moisture. Spread in a standard (about 9″) pie pan greased on the bottom with 1 ½ tablespoons butter or oil. Press down to form a crust on the bottom only and bake about 15 minutes, until the edge of the crust starts to brown. Reduce oven temp to 375 and position rack in middle.

Meanwhile, heat 1 ½ tablespoons butter or oil in a 10 inch skillet over medium high. Add onion and cook, stirring frequently, until golden in most places. It should sizzle loudly as it cooks for about 10 minutes, if the burner is hot enough. Remove to a medium mixing bowl.

Heat remaining (2 tablespoons) butter or oil in the same skillet over medium. Add mushrooms and sauté, stirring infrequently, until they brown and the released liquid evaporates, about 10 more minutes. Add to bowl with onion and season with ½ teaspoon salt and ¼ teaspoon pepper.

Brush baked crust with dijon. Top with mushroom/onion mixture almost to the edge.

Wipe clean the bowl from the vegetables, then add mascarpone, milk, eggs, and ¼ teaspoon each salt and pepper, and whisk until smooth. Stir in fontina. Pour over the tart, gently spreading out the fontina if it piles in the center. Top with a pinch of dried thyme or tomato slices, followed by a layer of parmesan, if using.

Place tart on a rimmed baking sheet and cook about 30 minutes, until nearly set but slightly soft in the middle. If you’re using a different pan size, such as for a double recipe, check the tart earlier and be prepared for less or more cook time.

Allow to cool before serving so the tart can set up more, making it easier to slice.