Remove radish leaves and place in a bowl of ice-cold water. Swirl around with your hand to remove all dirt from the leaves. Lay on a paper towel to dry.
Cut radishes in half and place in a mixing bowl. Drizzle with olive oil and add kosher salt. Place on a baking sheet cut-side-down and bake at 425 degrees for 25-30 minutes. Radishes should be tender when poked with a knife.
Meanwhile, add butter to a skillet over medium-high heat. Stir frequently with a wooden spoon until butter begins to darken, about 5 minutes. Stir in fresh rosemary. Keep on heat until butter turns golden brown, about 3-4 minutes, and then remove from heat.
Once radishes are roasted, add them to radish greens. Add the rosemary-infused brown butter. Toss together and serve.