Using a mallet, gently pound each pork chop between two sheets of plastic wrap or wax paper until it is about 1/2 inch thick. Season with salt and pepper and lightly dredge in flour, shaking off any excess.
In a large skillet, heat 2 tablespoons of oil over medium heat. Place 3 chops in the pan and cook until the edges turn golden brown, about 4 minutes. Turn over and cook the other side for 3 to 4 minutes. Transfer to a plate and cover loosely with foil. Repeat with the other 3 chops, adding the remaining oil.
To make the sauce: Deglaze the pan by adding the juice, cider, and 3/4 cup water, stirring any crystallized juices left clinging to the bottom (use a wooden spoon to prevent scratching). Bring to a boil, add the carrots, and let simmer until syrupy, about 12 to 13 minutes. Remove from heat, swirl in the butter, and add the thyme. Season to taste with salt and pepper. Spoon the sauce over the chops and serve. (Note: A perfectly cooked pork chop will be moist and slightly rosy. This color is completely safe.)