Place each chicken breast between two sheets of plastic wrap. Pound with a meat mallet to about 1/4-inch thickness.

Cut each breast into three 'tender-size' pieces. Season both sides with salt, pepper, and onion powder.

Dredge each piece lightly in flour and set aside on a plate. Shake off excess flour.

Heat 3 tbsp butter and 1 tbsp olive oil in a large deep skillet over medium-high heat. Add the dredged chicken in a single layer and sauté until golden, about 4 minutes per side. Remove chicken to a plate and tent with foil.

In the same skillet, add the remaining 1 tbsp olive oil. Add mushrooms, minced garlic, and a dusting of onion powder. Sauté until mushrooms begin to brown, about 4–6 minutes.

Pour in 1 1/2 cups dry white wine, scraping the browned bits from the pan with a wooden spoon. Return the chicken to the skillet and sprinkle with parsley. Bring to a boil, then reduce heat, cover, and simmer for about 15 minutes (this finishes the chicken and lets flavors meld).

Remove the chicken again and set aside. Add 1/2 cup heavy cream to the skillet and warm gently.

Over low heat, stir in 1/2 cup shredded asiago cheese, stirring constantly until the cheese melts and the sauce thickens to a smooth consistency. Adjust salt and pepper to taste.

Return the chicken to the pan, spoon the sauce over the pieces, heat through for 1–2 minutes, and serve immediately.