Bring broth to simmer in Dutch oven over medium-low heat. Whisk in 1 tablespoon butter until melted. Add carrots, radishes, Brussels sprouts, 1 teaspoon salt, and ½ teaspoon pepper to pot. Cover and cook, stirring occasionally, until vegetables are tender, 11 to 14 minutes. Using a slotted spoon, transfer vegetables to serving dish.
STEP 2
Remove all but ¼ cup broth from pot. Whisk remaining 3 tablespoons butter into remaining ¼ cup broth in pot until melted and slightly thickened and pour over vegetables. Season with salt and pepper to taste. Sprinkle with chives. Serve.