Combine the sugar and 1/4 cup salt in a shallow bowl; whisk in 3 cups water. Pierce the pork all over with a fork, then add to the bowl and soak 10 minutes. Remove and pat dry.
Put the flour on a plate. Season the pork with pepper, then dredge in the flour. Heat the olive oil in a large cast-iron skillet over medium-high heat; add the pork and cook, undisturbed, until golden on the bottom, 5 minutes. Add the sage to the skillet; flip the pork chops so they rest on top of the sage. Scatter the garlic, lemon slices and pepperoncini around the pork. Cook, undisturbed, until golden on the other side, about 5 more minutes.
Add the tomatoes, chicken broth and 1/2 cup water to the skillet and reduce the heat to medium low. Simmer, flipping the pork halfway through, until the liquid is reduced by half and the meat is tender, about 15 minutes. Serve with the couscous; top with the parsley.