Broccolette has wonderful fresh, sweet flavor, and the stalk is tender enough that you can use the whole piece, so there's no waste. At the store, select broccolette with stalks of even thickness so that they cook at the same rate. The zest of a lemon really brightens the flavor of this soup. A dollop of crème fraîche and a sprinkle of toasted almonds give a bit of elegance to the soup, but the garnishes are optional.
Cut the broccolette florets from the stalks and set them aside. Cut the stalks into 1-inch pieces and keep them separate from the florets. If some of the stalks are thick, cut them in half lengthwise.
Place a large saucepan over medium heat. Add the oil and onion, and cook, stirring frequently, until the onions are soft, about 8 minutes. Stir in the garlic and broccolette stalks only, and raise the heat to medium-high. Add the chicken stock and bring the soup to a simmer. Partially cover the pan, and lower the heat to maintain a simmer. Cook until the broccolette stalks are crisp-tender, 5 to 7 minutes. Add the florets and cook for another 2 or 3 minutes. Remove the saucepan from the heat, uncover, and let the soup cool for 10 minutes.
Transfer the soup to a food processor or blender, add the lemon zest, and purée until smooth. Return the soup to the pan, and season to taste with salt and pepper. Reheat gently over low heat.
Divide the soup among 4 bowls and garnish each serving with a tablespoon of crème fraiche and a scattering of almonds, if desired. Serve hot.