Pound chicken lightly between sheets of plastic wrap if needed for thick pieces. Cutlets are recommended if you can find them and won’t need to be pounded.
Pat chicken dry with paper towels and sprinkle each side with salt, pepper and paprika. Heat a large skillet over medium-high heat. Melt 1 tablespoon of butter and 1 tablespoon of olive oil in the skillet.
Add chicken to the skillet; you may need to do this in batches so you don't overcrowd the pan. Cook several minutes on each side, until seared and just barely cooked through (160-165 degrees). Transfer to a plate and tent with foil to keep warm, then repeat with the rest of the chicken. Add another pat of butter if needed.
To the skillet, add another tablespoon of butter and swirl it around to melt. Pour in ¼ cup of chicken broth and use a wooden spatula to stir, scraping up the brown bits on the bottom of the skillet as you go.
Bring to a low boil and let simmer over medium heat for 3-4 minutes or until sauce is reduced by half. Whisk in Dijon mustard and remaining 1 cup of chicken broth. Simmer until thickened, then remove from heat and stir in the sour cream. Settle chicken back into the same pan with the sauce, and spoon some over the top. Sprinkle with fresh minced parsley and serve immediately with mashed potatoes and sautéed veggies. Garnish with fresh minced parsley if desired.