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Sprinkle salt over chicken breasts. Cover with place in fridge while preparing topping.
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Preheat oven to 425 degrees F.
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Put bread, 3 tablespoons softened butter, 2 tablespoons parsley, garlic, shallot, thyme, and pepper in a food processor. Pulse until fully combined.
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{Monica puts her shallot in the sauce. I wasn't paying attention and put it in the topping. You can’t go wrong either way.} My topping was more paste like. Monica’s topping looked bready and fluffy. Either way the flavor rocks and that’s what’s important.
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Whisk together cream, chicken broth, wine, and mustard.
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Pat chicken dry and season with pepper. Arrange chicken in an X (for 4 breasts, or side-by-side for 2 breasts) in a large skillet. Brush the chicken with melted butter, then distribute the topping evenly between the chicken. If you topping is more paste-like too, press i down some to cover the entire breast.
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Carefully pour 3/4 of the cream mixture into the pan around the chicken.
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Bake 30 to 35 minutes, until topping ir golden brown and chicken is cooked through.
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Gently remove chicken from the pan; set aside and keep warm.
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Add the rest of the cream mixture to the pan and whisk. Bring to a boil over medium-high heat. {Be careful, the skillet handle will be HOT!}
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Cook until thickened, about 5 minutes. Remove from heat and season with remaining parsley, salt and pepper.
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Serve chicken over mashed potatoes, top with plenty of sauce, and a little sprinkling of parsley.