Pat chops dry with paper towels and season with salt and pepper. Heat oil in large non stick skillet over medium high heat until just smoking. Cook chops until well browned. About 5 minutes each side. Transfer to platter and tent with foil.
Toss the pears with sugar, 1/4 teaspoon salt and 1/8 teaspoon pepper in bowl. Add pear slices, cut side down, to empty skillet and cook until golden and beginning to soften, 1 to 2 minutes per side. Add broth and simmer until pears are softened, about 2 minutes. Transfer to platter with pork.
Continue to cook until sauce is slightly thickened, 1 to 2 minutes. Off heat, stir in butter and vinegar. Season with salt and pepper. Spoon sauce over pears and chops. Top with cheese.