Chef John's Chicken French

Step 1
Beat eggs and milk together in a shallow bowl. Whisk flour, salt, black pepper, and cayenne pepper together in another shallow bowl.

Step 2
Gently press chicken into flour mixture to coat; shake off excess flour. Dip into egg mixture and coat completely.

Step 3
Heat olive oil and 1 tablespoon butter together in a large skillet over medium heat. Cook chicken in hot oil until lightly browned, 2 to 3 minutes per side. Transfer chicken to a plate.

Step 4
Cook and stir vegetable broth, sherry, and lemon juice in the same skillet; bring to a boil and cook until sauce is reduced by half. Remove from heat and add cold butter chunks; stir until butter is melted and sauce is shiny and thickened, 1 to 2 minutes. Stir parsley into sauce and season with salt and pepper.

Step 5
Return chicken to the skillet over medium heat, spoon sauce over the top, and cook until chicken is heated through and no longer pink in the center, 1 to 3 minutes more.