01 - Pat chicken breasts dry with paper towels, season both sides generously with salt and pepper. Lightly dredge each breast 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 internal temperature reaches 165°F. Transfer to a plate and cover loosely with foil.
03 - Add remaining 1 tablespoon butter to the skillet. Add sliced mushrooms and sauté for 4–5 minutes, stirring occasionally, until they release moisture and develop golden brown edges. Stir in shallot and garlic; cook 1 minute until fragrant.
04 - Pour in white wine, using a wooden spoon to scrape up browned bits from the bottom of the skillet. Let simmer for 2 minutes until slightly reduced, then 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 and any accumulated juices to the skillet. Spoon sauce and mushrooms generously over the chicken. Simmer gently for 2–3 minutes until chicken is heated through. Garnish with fresh parsley and additional Asiago cheese if desired.