Start by preheating your oven to 425°F (220°C) and lining a baking sheet with parchment paper. Trim the leafy ends from the radishes and cut larger ones in half. This ensures they cook evenly and develop a golden roasted texture.
Place the radishes on the prepared baking sheet and drizzle them with olive oil. Sprinkle kosher salt, cracked black pepper, and garlic powder over the top. Toss everything gently with your hands until each radish is well coated.
Spread the seasoned radishes in a single layer on the baking sheet. Roast them in the preheated oven for about 20–25 minutes. During roasting, the radishes soften, their sharpness mellows, and they develop a subtle sweetness.
While the radishes are roasting, combine Greek yogurt, chopped chives, garlic powder, salt, and pepper in a medium bowl. Use a spatula to fold the ingredients together until smooth and well blended. Set the sauce aside until ready to serve.
If you want extra richness, melt butter in a small skillet over medium heat. Stir occasionally as it foams and turns golden brown. Once it develops a nutty aroma and brown specks, remove it from the heat immediately.
Spread the garlic chive yogurt onto a serving platter in an even layer. Place the roasted radishes on top, then drizzle with the brown butter if using. Finish with lemon zest and a sprinkle of flaky sea salt before serving.