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Place the pan you used to sear the pork over medium heat. If the pan is dry, add 1-2 teaspoons olive oil.
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Saute the shallot until just translucent, 1-2 minutes.
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Add the balsamic and water, scraping the bottom of the pan to pick up all the fond.
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Stir in the sugar allow the sauce to reduce until just thickened.
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Remove from the heat and gently whisk in the butter until melted and combined.
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Season with salt and pepper to taste.
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Drizzle the pan sauce over the pork chops and top with a sprinkling of pomegranate arils.
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Serve with the roasted brussels sprouts!