Pound the chicken breast with a meat mallet between two sheets of waxed paper or plastic wrap until the meat reaches a uniform thickness of about 1/4-inch. Cut the chicken into serving-sized pieces, typically two or three pieces per breast for even cooking.

In a deep, heavy skillet or sauté pan, heat the butter along with one tablespoon of olive oil over medium heat. Dredge each piece of chicken in seasoned flour before adding it to the hot oil and butter mixture in the skillet. Sauté until golden brown on each side, which should take about five minutes per side. Once done, remove the chicken from the pan and set it aside.

Add the remaining tablespoon of olive oil to the hot skillet where you cooked the chicken. Sauté the mushrooms and minced garlic until the mushrooms begin to brown nicely, absorbing all those flavorful residues left in the pan from cooking the chicken.

Pour in the dry white grape juice while scraping up all those delicious browned bits from the bottom of the pan; this process is known as deglazing. To enhance flavor, bruise three sprigs of fresh thyme by twisting them between your fingers before adding them to the skillet with mushrooms.

Return the sautéed chicken back into the pan with mushrooms and thyme mixture. Bring everything to a boil, then reduce heat to low, cover, and let it simmer gently for about fifteen to twenty minutes so that all flavors meld beautifully.

Once simmering is complete, remove the chicken from the pan again and incorporate heavy cream into the remaining mixture while heating through. Stir in shredded asiago cheese—feel free to adjust based on your preference for cheesiness—and continue cooking over low heat until melted and combined into a rich sauce that coats your chicken elegantly.