1. Cook bacon in large skillet over medium-high heat until crisp, about 5 minutes. Transfer bacon to paper towel-lined plate and pour off all but 1 tablespoon fat from skillet. Pat chops dry with paper towels and season with salt and pepper. Cook chops in empty skillet until well browned and cooked through, about 5 minutes per side. Transfer to plate and tent with foil.
2. Add shallots and sage to now-empty skillet and cook until softened, about 2 minutes. Add garlic and cook until fragrant, about 30 seconds. Add broth, 3 teaspoons vinegar, and any accumulated pork juices, scraping up any browned bits. Simmer until reduced by half, 3 to 5 minutes. Off heat, whisk in butter, remaining vinegar, and bacon. Season with salt and pepper. Pour sauce over chops. Serve.