Heat oil in a large nonstick skillet over medium-high heat. Season the pork chops with 1/2 tsp salt and a few grinds of black pepper. Cook until browned, 3 minutes per side. Transfer to a plate.
Add the red onions to the skillet and season with salt. Cook, stirring until lightly browned, 3 minutes. Reduce the heat to medium; stir in the flour and cook, stirring 2 minutes. Add the chicken broth and bay leaf. Cook, stirring until thickened, about 3 minutes. Add the vinegar and stir well and return the pork to the skillet to heat through.
Meanwhile, bring 2 1/4 cups water to a boil in a medium saucepan over medium-high heat. Add the grits and 1/2 teaspoon salt. Reduce the heat to low and cook, stirring, until thickened, 5 minutes. Stir in the cheese.
Remove the pork from the skillet, discard the bay leaf and stir in the parsley in the pan sauce. Serve the pork with the grits. Top with the pan sauce and garnish with more parsley.