If chicken breasts are large, slice in half horizontally to create thin cutlets (see how-to). Season with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add chicken breasts to skillet and cook until golden brown, approximately 3 minutes. Flip and reduce heat to medium-low. Continue cooking until golden brown and chicken reaches an internal temperature of 165 degrees F. Remove chicken from skillet to a plate and cover with aluminum foil to keep warm.

Remove skillet from heat and carefully pour in the wine (or chicken broth), scraping up the brown bits. Return skillet to medium-low heat. Add the butter and melt. Stir in the flour. Slowly whisk in the broth. Simmer until the liquid is reduced by half. Stir in the Dijon mustard and parsley. Add salt and pepper to taste if desired.

Spoon Dijon sauce over chicken and serve.