Heat a large saute or frying pan to medium-high heat. Add the olive oil and carefully place the Brussels Sprouts cut-side down in the pan.
Cook 4-6 minutes or until the Brussels Sprouts start to brown. Season with the salt and pepper, all the while keeping the Brussels Sprouts cut-side down to brown (don't stir yet).
Add the chicken broth and stir to combine. Cook until most of the broth is cooked out and the Brussels Sprouts are sizzling and browning again, about 4-6 minutes.
Add the garlic and cook for one more minute until the garlic is fragrant and the chicken broth has cooked out.