Season the pork chops generously on both sides with salt and pepper. Heat a cast iron skillet over medium high heat. Add a Tablespoon of butter to the skillet and let it melt. Place two pork chops in the skillet and sear for 3-4 minutes until browned. 

Flip pork chops and sear for an additional 3-5 minutes or until a thermometer inserted in the meat reads 145 degrees. Remove the chops from the skillet, cover with foil, and set aside. Add the second Tablespoon of butter to the skillet, and repeat the searing process with the second two chops. 

To make the sauce, add the balsamic to the skillet and use a spatula to scrape any browned bits off the bottom of the pan. Add the shallots to the pan and cook for about 2 minutes until softened. Add the tomatoes and 1 Tablespoon butter and cook, stirring often, until the tomatoes are cooked down and the sauce is thickened. Season to taste with salt and pepper.

Nestle the pork chops back into the skillet and cover with the sauce. Remove from heat and sprinkle with fresh basil. Serve immediately.