For the crust, combine the flour, cornmeal, salt, and butter in a food processor and pulse until it resembles coarse sand.
Add the egg and continue pulsing until the dough starts to clump together (like wet sand).
Transfer the dough to a floured surface and shape into a flat circle. Roll the dough out into a 12” circle.
Transfer to a 9” tart pan and press into the bottom and sides. Remove any excess dough from the top.
Place in the freezer for about 30 mins.
Preheat oven to 375°F. Lightly grease one side of a 12” square of foil. Press the foil, greased side down, against the bottom and sides of the crust.
Bake for 10 mins, carefully remove the foil and continue baking for 5-8 mins, until lightly golden brown around the edges. Cool on a wire rack.
Reduce oven temperature 350°F.
Heat the olive oil and butter in a large skillet over medium heat.
Sauté the shallots for 2-3 mins, until softened. Stir in the garlic and thyme and sauté for 30 seconds.
Increase heat to medium-high and add the mushrooms. Cook the mushrooms for 9-10 minutes, stirring occasionally, until they’re tender and the liquid has evaporated. Season with 1/2 tsp salt and pepper to taste.
Transfer to a plate and let cool.
Place the mascarpone cheese in a medium bowl. Slowly pour in the milk and whisk until smooth. Whisk in the eggs, shredded cheeses, and 1/2 tsp salt then stir in the cooled mushrooms.
Pour the mixture into the tart shell and bake for 35-40 mins, until a knife inserted in the center comes out clean.
Allow the tart to cool for at least 10 minutes before removing from the pan.