Chicken and Mushrooms in Creamy Sauce (Skillet Dinner)

Ingredients

• 2 large boneless skinless chicken breasts, about 1 1/2 lb (680 g) total
• 1 teaspoon kosher salt, divided
• 1/2 teaspoon black pepper, divided
• 1/4 cup (30 g) all-purpose flour
• 1 tablespoon olive oil
• 1 tablespoon unsalted butter
• 2 tablespoons unsalted butter
• 10 oz (280 g) cremini mushrooms, sliced
• 1 small shallot, finely chopped
• 3 cloves garlic, minced
• 1/4 cup (60 ml) dry white wine, or extra chicken stock
• 1/2 cup (120 ml) low-sodium chicken stock
• 1 cup (240 ml) heavy cream
• 1/3 cup (30 g) finely grated parmesan cheese
• 1 tablespoon chopped fresh parsley
• 1 teaspoon fresh lemon juice, optional