Preheat the oven to 425 degrees F (220 degrees C).
Cut greens from radishes. Rinse and soak greens until all grit is removed and the water is clear; set aside to dry. Rinse and dry radishes; cut in half.
Stir butter, 1 teaspoon garlic, salt, and pepper together in a medium bowl. Add radishes and toss to coat. Arrange radishes, cut-sides down, on a baking sheet.
Roast in the preheated oven until radishes are soft enough to easily cut through with a fork, 15 to 20 minutes.
While radishes are roasting, heat olive oil in a large skillet over low heat. Sauté onion in hot oil until almost soft, about 5 minutes. Add greens and remaining 1 teaspoon garlic. Sauté until greens are wilted, 5 to 8 minutes.
Divide sautéed greens and onions among serving plates and top with roasted radishes.