In a large skillet melt the butter over medium heat. Put the garlic cloves in the skillet and brown completely. Remove the garlic to a small bowl. Add the bacon to the skillet and cook until crisp. Transfer the bacon to paper towels to drain, then cut into small pieces and set aside.
Put the sprouts in the skillet with bacon grease, flat side down, and saute until they begin to brown, about 2 to 3 minutes. Turn them over, increase the heat to medium-high and add the sugar and the broth. Cook for a few minutes, then add the cooked bacon and the garlic cloves. Cover and cook for 2 more minutes. Transfer to a serving bowl and serve.