Add 1 cup of the water, the brown sugar, kosher salt, and garlic to a small saucepan over medium heat and cook, stirring often, until the sugar, salt, and garlic has dissolved in the water.
Pour the contents of the saucepan into a container along with the 2 cups of cold water then submerge the pork chops in the water and refrigerate for about 45 minutes.
Preheat the oven to 400°F.
Remove the pork chops from the brine then pat dry with paper towels.
Season the pork chops all over with the 1 tsp of black pepper.
Heat the oil in a cast-iron skillet over medium-high heat.
Carefully add the pork chops to the pan and sear for 2-3 minutes then turn the pork chops over and sear the other side 2-3 minutes.
Turn each pork chop on its side and sear all around.
Put the skillet in the preheated oven and bake until the pork chops reach an internal temperature of 140°F, 15 to 20 minutes.
Take the skillet out of the oven then transfer the pork chops to a plate and tent with aluminum foil.
Put the skillet back on the stove over medium-high heat and add the onion, garlic, mushrooms, and 1/4 tsp salt then cook, stirring often, until mushrooms have browned, about 4 minutes.
Add the butter to the skillet and when melted stir in the flour then reduce the heat to low and stir in the water until well combined.
Stir in the heavy cream and vinegar until heated through and gravy has thickened.
Taste the gravy and season with additional salt & pepper if needed.
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