Move oven rack to middle position and heat oven to 425°F.
Cut radishes into halves (if they're on the small side) or quarters (if they are large). Put the radishes in a medium bowl.
Heat anchovy and butter together in a small bowl for 30 seconds in the microwave. Stir until butter is melted.
Add anchovy butter mixture, salt, and 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.