1. Pat the chicken thighs dry with paper towels, then season both sides with the salt and black pepper.

2. Heat the olive oil and 1 tablespoon of the butter in a large skillet over medium high heat.

3. Add the chicken thighs in a single layer and sear for 4 to 5 minutes per side, until deep golden and mostly cooked through. Transfer the chicken to a plate and set aside.

4. Reduce the heat to medium and add the remaining 1 tablespoon butter to the same skillet.

5. Stir in the sliced mushrooms and cook, stirring occasionally, for 5 to 7 minutes until they release their moisture and become browned and tender.

6. Season the mushrooms with a small pinch of salt and pepper, then add the minced garlic and thyme and cook for 30 seconds until fragrant.

7. Pour in the chicken broth and use a wooden spoon to scrape up the browned bits from the bottom of the pan. Let the mixture simmer for 1 to 2 minutes.

8. Stir in the heavy cream and Dijon mustard, if using, and bring the sauce to a gentle simmer over medium low heat. Do not let it boil.

9. Turn off the heat and gradually sprinkle in the Asiago and Parmesan cheese, stirring constantly until the cheese has melted and the sauce is smooth and creamy.

10. Return the seared chicken thighs and any accumulated juices to the skillet, nestling them into the sauce.

11. Simmer on low for 5 to 8 minutes, spooning the sauce over the chicken, until the chicken is cooked through and the sauce has thickened to your liking.

12. Taste and adjust seasoning with additional salt and pepper if needed, then garnish with chopped parsley or extra thyme and serve hot with your favorite sides.