Place the bacon in a large, deep skillet, and cook over medium-high heat, stirring occasionally, until evenly browned, but not crispy, about 10 minutes. Remove the bacon with a slotted spoon, leaving the grease in the skillet. Pour off all but 2 tablespoons of the bacon grease and stir in the olive oil, butter, onion, and garlic. Season with salt and pepper. Cook and stir until the onion softens and the garlic lightly browns, 5 to 7 minutes.
Stir in the balsamic vinegar and bring to a simmer; cook until the liquid has reduced by 1/3. Add the reserved bacon, the halved Brussels sprouts, and the chicken stock. Stir, then bring to a boil over high heat. Reduce heat to medium-low, and simmer until the Brussels sprouts are tender, yet still slightly firm, about 10 minutes.
