Blend flour and salt in processor. Drop in butter and pulse until mixture resembles coarse meal. Add cold water to blend dough. Gather dough into ball; flatten into disk. Wrap in plastic, chill 45 minutes.
Roll out dough on floured surface to 12-inch round. Transfer to 9-inch-diameter tart pan with removable bottom. Trim edges, leaving ½-inch overhang. Fold overhang in to form double-thick sides. Press tart edges to raise dough 1/8 inch above pan. Pierce crust with fork and transfer to refrigerator to chill for 30 minutes.
Peel and remove the root ends from the shallots. Slice them in quarters and place on a small sheet pan. Pour 2 tablespoons of olive oil, balsamic vinegar, 1 teaspoon salt and ¼ teaspoon pepper over top. Roast until the onions are soft, about 45 minutes. Remove from oven and set aside until ready to use.
In a large skillet over medium heat, melt the butter. Add mushrooms, and remaining black pepper; sauté for about 10 minutes until golden. Remove from the heat.
Mix 2 egg yolks (reserve the egg whites), ricotta, cream, ½ cup Parmesan cheese, chives, and the remaining 1 tablespoon olive oil. Remove the tart shell from the refrigerator. Spread the ricotta mixture evenly across the bottom of the tart shell. Add the shallots and mushrooms on top. Sprinkle the remaining Parmesan evenly over the top of the shallot and mushroom filling.
In a small bowl, combine the reserved egg whites, 2 eggs, and the cream. Pour over the mushroom filling. Cover the tart with foil and bake for 30 minutes. Remove the foil and bake another 15 minutes, until the top is bubbling and the crust is slightly brown.
Finish off with fresh thyme or micro herbs. Serve warm or at room temperature. Enjoy!
Notes
Store-bought pie crust can be used instead of homemade crust.