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Rub chicken breasts with the dijon mustard on both sides (TIP: I've added the chicken breasts to a Ziploc bag and then tossed them in the mustard that way, but rubbing them by hand is fine)
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Salt and pepper both sides of chicken
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Heat butter in dutch oven (or skillet) over Medium to Medium-High heat
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Once butter is sizzling a bit, add chicken and sear on Medium-High for 2-3 minutes on each side
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Lower heat to Low-Medium, and add lemon juice over the chicken
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Cover dutch oven or skillet with lid and cook over Low-Medium heat for 12-15 minutes (depending on the thickness of the chicken breasts and the heat of your stovetop)
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Once the chicken breasts have cooked through, take them out and cover with foil for about 5 minutes to rest. Slice chicken breasts diagonally, and drizzle lemon-dijon pan "sauce" over them
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Serve with sautéed green beans (TIP: After quickly sautéing, add them to the remaining dijon-lemon sauce in dutch oven, and then season with salt and pepper)