Chef John's Chicken French

Ingredients (14)

• + 4 eggs add to pantry
• + 2 tablespoons milk add to pantry
• ✓ 1 cup all-purpose flour
• + 1 tablespoon salt add to pantry
• + 1 teaspoon ground black pepper add to pantry
• + 1 pinch cayenne pepper add to pantry
• + 1 ½ pounds skinless, boneless chicken breast cutlets, pounded flat add to pantry
• ✓ 2 tablespoons olive oil
• ✓ 1 tablespoon butter
• + 1 cup vegetable broth add to pantry
• + ½ cup dry sherry add to pantry
• + 2 lemons, juiced add to pantry
• + ¼ cup cold butter, cut into chunks add to pantry
• + 1 tablespoon chopped fresh flat-leaf parsley add to pantry