Preheat the oven to 200˚F. Place the first 6 ingredients in a small bowl, whisk to combine and set aside.
Heat the oil in a large skillet set over medium-high. Season the pork with salt and pepper and cook 3 to 4 minutes per side, or until cooked through with just a hint of pink in the middle. Set pork chops on a baking sheet and keep warm in the oven.
Drain the fat from the skillet, add the walnuts and toast them 2 to 3 minutes. Now pour in the pomegranate mixture, bring to a simmer, and simmer 2 minutes, until a thickened sauce forms. Season the sauce with salt and pepper. Plate the pork, top with sauce and serve.