Season the Chicken: Pat the chicken breasts dry with paper towels. Season both sides with salt and black pepper.
Sear the Chicken: Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 4-5 minutes on each side, until golden brown. Remove the chicken and set aside (it will finish cooking later).
Sauté the Mushrooms: In the same skillet, reduce the heat to medium and add the butter. Once melted, add the sliced mushrooms and sauté for 5-7 minutes until browned and softened.
Add Garlic: Stir in the minced garlic and cook for an additional minute, until fragrant.
Make the Sauce: Pour in the chicken broth, scraping the bottom of the skillet to deglaze and release any browned bits. Stir in the heavy cream, Asiago cheese, thyme, and red pepper flakes (if using). Let the sauce simmer for 2-3 minutes, stirring occasionally, until slightly thickened.
Return the Chicken: Add the seared chicken breasts back into the skillet, spooning the sauce over the top. Reduce the heat to low, cover, and simmer for 8-10 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Garnish and Serve: Remove the skillet from heat and garnish with fresh parsley. Serve hot with the creamy mushroom Asiago sauce over pasta, rice, or mashed potatoes.