Set the oven rack to middle position and preheat to 350°F. Line a rimmed baking sheet with parchment paper. (Alternatively, you can use a mini-muffin pan.)

In a large non-stick skillet, heat the oil and butter over medium-high heat. Add the shallots and garlic and sauté until fragrant, about 2-3 minutes. Add the mushrooms, salt, pepper, and crushed red pepper (if using) and continue to sauté until they have release their liquid and become soft, about 5-7 minutes. Add the thyme and parsley and stir to combine. Transfer the mushroom mixture to the bowl of a food processor.  Add the cheese and crème fraîche. Pulse the mixture until mushrooms are 1/4-inch bits, about 5 (1 second) pulses. Transfer the mixture to a medium bowl and season to taste with salt and pepper.

Place the mini-phyllo tarts on the prepared baking sheet or muffin tin and bake until crisp, about 3-5 minutes. Divided the mushroom mixture evenly (about 1 1/2 teaspoons) in the warm tarts. Garnish with thyme and parsley and serve. Tarts can be kept in a warm oven until ready to serve.  Enjoy!