Season the chicken with salt and pepper and dust lightly with flour on both sides. Sprinkle a few dashes of paprika on the “top” side for a bit of additional color.
In a 10” – 12” deep skillet, melt the butter with the oliveoil over medium-high heat. Add the pieces of chicken, “top” side with paprika down first. Brown slightly, then turn to brown the other side. Transfer to a plate and set aside. (Cooking will be completed in the mustard sauce.)
Add the onion to the same skillet and cook over medium-high heat, scraping up any browned bits from the chicken and stirring occasionally until softened, about 8 minutes. Add the 1 teaspoon of flour and stir for about a minute, then add the mustard and chicken broth. Bring to a slow boil.
Add the chicken pieces back to the skillet, nestling in amongst the onions. Cover and simmer over medium heat until the chicken is cooked through, about 10 minutes.