Step 1: Preheat the oven to 350F.
Step 2: Place a baking sheet near the stove, ready for the chicken.
Step 3: Season the chicken breasts on both sides with salt and pepper.
Step 4: Pour the flour onto a large plate and dredge the chicken breasts until well coated. Shake off the excess.
Step 5: In a large skillet over medium high-heat, heat the butter and oil. When the butter has melted and looks foamy, add the chicken. (Work in batches if your pan isn't big enough so that you don't crowd the pan.)
Step 6: Brown the chicken for 3 minutes per side, or until golden.
Step 7: Transfer the chicken to the baking sheet and place in the oven for 5 minutes (longer if the chicken breasts are thick), or until a thermometer inserted into the thickest part of a breast registers 165 degrees.
Step 8: If the chicken is done before the sauce, transfer it to a serving platter and tent it loosely with foil to keep warm.
Step 9: While the chicken finishes cooking, return the skillet to medium heat and add the wine. Be careful since the oil in the pan will sputter a little when you add the wine. Cook for 5 minutes, or until the wine is reduced by about half.
Step 10: Add the cream and simmer for 2 to 3 minutes, or until the sauce coats the back of a spoon.
Step 11: Stir in the mustard, capers and parsley, reserving a little parsley for sprinkling over top. Taste and add more salt and pepper, if you like.
Step 12: Place each chicken breast on a plate, drizzle with the sauce, and sprinkle with the remaining parsley.
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