3 tbsp. butter
2 large shallots, thinly sliced
11/4 lb. radishes—2 radishes cut into matchsticks and reserved for garnish, remaining radishes quartered—plus 2/3 cup finely chopped radish greens
1 large russet potato (about 10 oz.), peeled and chopped
3 cups chicken stock
11/2 cups whole milk
1/4 cup EVOO
1/4 cup finely chopped fresh basil leaves
3 tbsp. finely chopped fresh chives
1 tsp. lemon zest, plus 1 tbsp. juice (from 1 lemon)
1 clove garlic, finely chopped
1. 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
2. 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.
3. Transfer the soup to a blender. Puree the soup until creamy; season. Refrigerate until chilled, at least 2 hours.
4. Divide the chilled soup among 4 bowls. Drizzle with the radish greens pistou. Garnish with the matchstick-size radishes.