Pat the chicken breasts dry with paper towels. Butterfly them by carefully slicing horizontally through each breast almost to the other side, then open like a book and cut into two equal pieces. Season both sides with garlic powder, Italian seasoning, kosher salt, and freshly ground black pepper.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Once hot, add the chicken pieces and sear them until golden brown and cooked through, about 4 to 5 minutes per side. Remove the chicken from the skillet and set aside on a plate.

Reduce heat to medium and melt 1 tablespoon butter in the same skillet. Add sliced mushrooms and fresh thyme, seasoning lightly with kosher salt and pepper. Cook, stirring occasionally, until the mushrooms release their moisture and become golden brown, around 6 to 8 minutes. Add minced garlic and cook for 1 more minute until fragrant. Remove the mushrooms from the skillet and set aside.

Pour in the white wine and stir constantly to lift all browned bits off the bottom of the pan. Let the liquid reduce for about 2 minutes to concentrate flavor.

Melt the remaining 3 tablespoons of butter in the skillet. Whisk in the flour to form a paste and cook for about 30 seconds. Gradually whisk in the chicken broth and milk, stirring constantly to avoid lumps. Increase heat to medium-high; bring to a simmer then reduce to medium-low and cook, stirring occasionally, until the gravy thickens, approximately 5 minutes. Stir in grated Parmesan cheese, 1/4 teaspoon kosher salt, and freshly ground black pepper. Taste and adjust seasonings if needed.

Return the cooked chicken and mushrooms to the skillet, spooning the gravy over the top. Cover and simmer on low heat for 5 minutes to meld flavors and reheat the chicken through.

Garnish with fresh thyme leaves and serve hot over mashed potatoes or egg noodles for a complete comforting meal.