For the pork chops: Pat the pork chops dry with a paper towel and season each side with a generous amount (a 4-finger pinch) of each salt and black pepper. Let rest for 10 minutes at room temperature.
In a large skillet, heat the butter and canola oil over medium-high heat. When the oil begins to smoke, gently place the pork chops in the skillet and cook until deep golden brown, 3 to 4 minutes per side. Transfer the chops to a baking sheet and roast until just rosy in the center and an instant-read thermometer inserted into the center of a chop registers 145 degrees F, 10 to 15 minutes.
Meanwhile, for the walnut romesco: Combine the garlic, roasted red pepper, bread, oil, Pecorino, walnuts, water, tomato paste, vinegar, salt and pepper in a food processor. Process until a finely chopped paste forms, adding more water a tablespoon at a time if needed. Transfer the sauce to a small saucepan and cook over medium-low heat, stirring often, until it is warm.
Serve the pork chops with the warm romesco. Sprinkle with parsley if using. Enjoy!