Heat the oil in a large nonstick skillet over medium-high heat. Season the pork with 1/2 teaspoon salt and a few grinds of 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, then return the pork to the skillet to warm 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 the parsley into the pan sauce. Serve the pork with the grits. Top with the pan sauce and more parsley.