1. Pat the chicken dry with paper towels, then season both sides with kosher salt and black pepper. Lightly dredge each piece in flour, shaking off the excess.

2. Heat the olive oil and butter in a large skillet over medium-high heat. When hot and shimmering, add the chicken in a single layer and sear until deeply golden on both sides, about 4–5 minutes per side. Transfer the chicken to a plate.

3. Add the sliced cremini mushrooms to the same skillet. Cook, stirring occasionally, until they release their juices and begin to brown, 5–7 minutes.

4. Stir in the chopped shallot, minced garlic, and chopped thyme. Cook for 1–2 minutes, just until fragrant and softened.

5. Pour in the white wine (or extra chicken broth) to deglaze the pan, scraping up any browned bits from the bottom. Let it simmer and reduce by about half.

6. Add the chicken broth and bring to a gentle simmer. Reduce the heat to medium-low, then slowly stir in the heavy cream. Add the grated Asiago cheese and Dijon mustard, stirring until the cheese melts and the sauce becomes smooth and slightly thickened.

7. Return the seared chicken and any accumulated juices to the skillet, nestling the pieces into the sauce. Spoon some sauce over the top of each piece. Simmer gently for 8–10 minutes, or until the chicken is cooked through and the sauce coats the back of a spoon.

8. Sprinkle the chopped parsley over the chicken. Taste the sauce and adjust seasoning with more salt and pepper if needed. Serve hot with plenty of creamy mushroom Asiago sauce over pasta, potatoes, or rice.