Chicken Scallopini - Miz En Place

Ingredients

• 16 ounces boneless, skinless chicken breasts
• 1-1/4 tsp kosher salt, divided
• 1 tsp black pepper, divided
• 1/2 cup all-purpose flour, divided
• 3 tbsp olive oil
• 4 tbsp unsalted butter
• 8 ounces sliced fresh cremini mushrooms
• 1/2 cup sliced shallots
• 1/2 cup dry white wine
• 1/2 cup heavy whipping cream
• 2 tbsp chopped fresh flat-leaf parsley
• 1/2 tsp grated lemon zest, plus more for garnish