Creamy Radish Soup with Radish Greens Pistou

In a large pot, melt the butter over medium heat. Add the shallots and cook, stirring occasionally, until softened, about 3 minutes. Add the quartered radishes and the potato; season with salt and pepper. Cook, stirring often, until the vegetables soften, about 5 minutes. Add the stock and milk and bring to a boil over high heat. Reduce heat to medium and simmer the soup until the vegetables are tender, about 15 minutes

Meanwhile, in a medium bowl, whisk the oil, basil, chives, lemon zest and juice, garlic, and the radish greens; season. Set the radish greens pistou aside.

Transfer the soup to a blender. Puree the soup until creamy; season. Refrigerate until chilled, at least 2 hours.

Divide the chilled soup among 4 bowls. Drizzle with the radish greens pistou. Garnish with the matchstick-size radishes.