01 - Pat the chicken breasts dry with paper towels. Season both sides generously with kosher salt and freshly ground black pepper. Dredge each breast lightly in flour, shaking off any excess coating.
02 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat until butter foams. Add chicken breasts and sear for 4–5 minutes per side until golden brown and cooked through (internal temperature reaches 165°F). Transfer to a plate and cover loosely with foil.
03 - Add remaining 1 tablespoon butter to the same skillet. Toss in sliced mushrooms and sauté for 4–5 minutes, stirring occasionally, until they release moisture and develop golden-brown edges. Add shallot and minced garlic; cook 1 minute until fragrant.
04 - Pour in white wine, scraping up browned bits from the bottom of the skillet with a wooden spoon. Let simmer for 2 minutes until slightly reduced. Add chicken broth and bring to a gentle simmer.
05 - Stir in heavy cream and grated Asiago cheese, whisking continuously until cheese melts completely and sauce becomes smooth and velvety. Simmer for 2–3 minutes until sauce coats the back of a spoon.
06 - Return chicken breasts along with any accumulated juices to the skillet. Spoon sauce and mushrooms generously over the chicken. Simmer gently for 2–3 minutes until everything is heated through. Sprinkle with fresh chopped parsley and serve immediately with additional Asiago and parsley for garnish.