Dissolve 1/4 cup salt and the sugar in 3 cups warm water in a large bowl. Insert a paring knife into the curved side of each pork chop to make a deep pocket, about 2 inches wide. Soak the chops in the brine, about 5 minutes. Meanwhile, finely chop the escarole and garlic. Toss with 2 tablespoons olive oil, and salt and pepper to taste. Remove the chops from the brine and pat dry. Fold each cheese slice and tuck into the pocket of a pork chop, then stuff with the escarole mixture. Brush the pork with olive oil, sprinkle with the sage and season with salt and pepper. Heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Sear the pork in batches, turning once, until golden brown, 3 to 4 minutes. Transfer to a plate. Add the beans and 1/3 cup water to the skillet, scraping up any browned bits; season with salt and pepper. Return the pork to the skillet, cover and cook over medium heat until no longer pink, 5 to 7 more minutes. Serve the pork with the beans.