Dry the pork chops well and season generously with salt and pepper. Heat a large cast iron pan over high heat and when hot, add the avocado oil. When the oil is hot, add the pork chops and cook until well browned and cooked through, about 4 minutes per side. Transfer to a serving plate and set aside. Do not clean the pan.

Add the shallots to the now empty pan and stir to scrape browned bits up and cook until soft, translucent, and just beginning to brown. Add the garlic and cook until fragrant, one minute more. Add the tomatoes and oregano and cook until tomatoes soften, about 2 minutes. Add vinegar and cook until the sauce reduces and becomes slightly syrupy, another 3 minutes or so. Add back any pan juices, stir and season to taste. If you would like it sweeter, add a touch of stevia or monk fruit. Off heat, whisk in butter, if using then pour sauce over the pork chops and sprinkle with cheese.