Move oven rack to middle position and heat oven to 425°F.
Cut 1 pound radishes into halves (if they're on the small side) or quarters (if they are large). Put the cut radishes in a medium bowl.
Heat 1 anchovy fillet and 1 Tablespoon unsalted butter together in a small bowl for 30 seconds in the microwave. Stir until the butter is melted.
Add the anchovy butter mixture, ½ teaspoon kosher salt, and ¼ teaspoon freshly ground black pepper to the radishes in the bowl. Toss together until the radishes are evenly coated.
Spread radishes over a small baking sheet. Bake for 20-25 minutes, stirring two to three times throughout cooking, until browned and tender. Serve immediately.