Preheat oven to 350 degrees Fahrenheit.
In a shallow dish combine the all-purpose flour along with the salt and pepper.
Fully dredge each chicken breast in the seasoned flour, patting off the excess.
Heat the oil in a large skillet over medium-high heat.
Add the chicken breast and cook golden brown (approximately 4 minutes per side). *Do not overcrowd the pan. You may have to do this in two batches.
Remove the browned chicken to a separate plate and tent it with foil to keep warm.
Add the minced shallot to the skillet, and cook until softened (about 1-2 minutes).
Stir in the chicken broth and the wine, scraping up any browned bits on the bottom of the skillet from browning the chicken.
Stir in the butter, dill, and mustard. Gently simmer the sauce for about 4-5 minutes to thicken slightly.
Add the chicken breast back into the skillet and spoon some of the sauce over each breast.
Place the chicken in a preheated 350-degree oven for 20-30 minutes, or until the chicken breasts reach an internal temperature of 165 degrees on an instant-read thermometer.