Place the Gorgonzola and butter in a blender. Pulse a few times until creamy smooth.
For the grilled radishes
Fire up your grill for direct cooking, 400 - 450 F.
Cut radishes in half. Place in a bowl. Drizzle with a little oil and season well with salt and pepper. Stir to coat.
Transfer to a grill basket or skewer if desired. You can also cook the radishes directly on the grill if they are large enough to not fall between the grates.
Place the radishes on the grill and cook over high heat 4-5 minutes per side or until lightly browned.
Serve immediately with the gorgonzola butter for dipping.