Recipe: Creamy Parmesan Garlic Mushroom Chicken

Name: Recipe: Creamy Parmesan Garlic Mushroom Chicken
Cuisine: European, Italian, Mediterranean
Ingredients: 4 boneless, skinless chicken breasts (about 2 pounds total), pounded to 1/2-inch thick; 1 tablespoon olive oil; 3 tablespoons unsalted butter; 10 ounces cremini mushrooms, thinly sliced; 1/2 medium yellow onion, diced; 1/2 teaspoon kosher salt, plus more for seasoning; 1/4 teaspoon freshly ground black pepper, plus more for seasoning; 4 cloves garlic, minced; 2 tablespoons all-purpose flour; 1 cup half-and-half or whole milk; 1/2 cup low-sodium chicken broth; 1/2 cup finely grated Parmesan cheese (about 1 ounce), plus more for serving; 2 tablespoons chopped fresh parsley leaves