Slice sweet red peppers and red onion into long strips. Pour olive oil into hot pan and then add the vegetables. Add salt and pepper and a tablespoon of sugar. Let them saute for 2 minutes, then add the red wine vinegar and olive oil. In another 2-3 minutes, add the chopped basil and stir for 30 seconds on the heat, then pour it into a bowl and set aside.
Place clean pan over medium high heat and add a tablespoon of olive oil. Make small cuts through the fat rind of the pork chops to keep them from curling up in the pan. Then season with an even layer of salt and pepper and press the salt and pepper into the meat. Crack the garlic with the palm of your hand or the flat of a knife so it just breaks open a bit and set aside.
When the pan just starts to smoke the olive oil it's ready for the pork chops. Place them carefully into the pan and scoot them a bit to make sure they wont stick. Add the cracked garlic and thyme to the pan. Slice in a few pads of butter, then use a spoon to scoop up the melted butter juices and baste over the top of the pork chops. Flip the chops after they've had 3-5 minutes on one side, then remove from pan after 3-5 minutes on the other side. Let them rest for 3 minutes more before serving.
