Step 1

Place 1/4 cup flour in a shallow dish. Sprinkle chicken with 1/4 teaspoon salt and pepper. Coat chicken in the flour, shaking off the excess. Discard any leftover flour.

Step 2

Heat 1 tablespoon oil in a large skillet over medium-high heat. Add the chicken and cook, turning once, until golden brown and cooked through, 2 to 4 minutes per side. Transfer the chicken to a plate; cover to keep warm.

Step 3

Add the remaining 1 tablespoon oil to the pan. Reduce heat to medium and add mushrooms and the remaining 1/4 teaspoon salt. Cook, stirring frequently, until the mushrooms are beginning to brown and soften, 4 to 6 minutes. Add garlic and cook, stirring, until fragrant, about 30 seconds more. Sprinkle the remaining 2 teaspoons flour over the mushrooms and stir to coat. Add wine and cook, stirring, until thickened and most of the liquid has evaporated, about 1 minute. Add half-and-half and cook, stirring, until the sauce is bubbling and thickened, 1 to 2 minutes. Remove from heat and top with Parmesan and parsley.