In the bowl of a food processor, combine the flour, salt, and pepper. Pulse once or twice to mix. Add the diced cold butter and pulse several times until the butter resembles small peas. Add the chopped rosemary and thyme.
Pour the ice water into the food processor while pulsing. Continue pulsing until the dough begins to stick together in small clumps. Check the dough, it should stick together if you squeeze it.
Dump the dough mixture onto the counter and use your hands to press it together into a large ball. Shape into a flat disc and cover with plastic wrap. Chill for at least 1 hour.
Preheat the oven to 400°F. Lightly grease a 10" tart pan with removable bottom. Roll the dough out on a lightly floured surface into a circle about 1 inch wider than the tart pan on all sides. Transfer the dough to the tart pan and press into the sides. Trim the edges.
Line the tart dough with foil and fill with pie weights or dried beans. Place the tart pan on a baking sheet. Bake for 15 minutes then remove the foil and pie weights.
Meanwhile, heat 2 tablespoons of olive oil in a wide skillet over medium high heat. Add the mushrooms and sauté until the mushrooms are tender and beginning to brown. If using more than one kind of wild mushroom, they can be sautéed separately in batches, using olive oil as needed. Transfer the mushrooms to a separate dish and set aside to cool.
In the same skillet over medium heat, add another tablespoon of olive oil. Add the diced shallots and sauté for 3 to 4 minutes until they are softened and beginning to brown. Add the minced garlic and chopped thyme, and sauté for another minute until fragrant. Transfer the shallots to a separate dish and set aside to cool.
In a mixing bowl whisk together the eggs and heavy cream. Add 1 tsp kosher salt and 1/4 tsp pepper along with the sautéed shallots. Stir in the shredded cheeses. Add the cooled mushrooms and stir together. Pour the mushroom filling into the par-baked tart shell and spread evenly.
Bake the tart for 40 to 45 minutes until the filling is set and the pastry is browned. Let the tart cool for a few minutes before lifting out of the tart pan and cutting into slices. Garnish with micro greens and enjoy!