Plant power. Pearl onions (like all onions) are rich in the antioxidant quercetin.
Melt 2 tablespoons of the butter with the oil in a large, deep skillet over medium heat. Add onions and sprinkle with 1/4 teaspoon of the salt. Increase heat to medium-high and cook, stirring occasionally, until liquid has cooked off and onions are beginning to caramelize, 10 to 15 minutes. Stir in broth, vinegar, and honey; bring to a boil.
Reduce heat to medium-low and simmer, stirring occasionally, for 10 minutes. Add remaining 1/2 tablespoon butter; cook until liquid has thickened and reduced to about 2 tablespoons and onions are caramelized, about 5 minutes. Sprinkle with pepper and remaining 1/4 teaspoon salt. Garnish with chopped chives, if desired.