In a container, mix 2 tablespoons salt with 4 cups cold water. Stir to dissolve salt. (The brine and chops can be placed in a Ziploc bag, removing air to completely submerge chops.) Place pork chops in the brine and refrigerate for an hour. Then remove them from the brine and pat dry with paper towels. Lay out the chops on a clean plate to allow them to come to room temperature.
Using a small knife, make a small incision in the side of the chop, pushing the blade into the center of the chop and moving the blade side to side to create a pocket while keeping the "mouth" as small as possible.
Create a filling by combining the poblano, cheese, salt and pepper. Stuff about a tablespoon of filling into each pork chop. Rub the outside of the chops with oil and season with salt and pepper.
Heat a cast-iron skillet over medium heat to the point where a droplet of water skitters around the pan. Place chops in the pan, cook about 5 minutes per side. The internal temperature should register about 145 degrees. Remove chops from the pan and allow them to rest for 5 minutes. Good served with rosemary mashed potatoes.