Classic Creamy Carrot Soup

Name: Classic Creamy Carrot Soup
Ingredients: For the Lemon-Herb Yogurt:; 1/2 cup (4 1/4 ounces; 120g) plain full-fat Greek yogurt; 2 tablespoons (30ml) fresh lemon juice from 1 lemon; 2 tablespoons (8g) finely chopped flat-leaf parsley leaves and tender stems; For the Carrot Soup:; 2 1/2 pounds (1.1kg) carrots (about 12 medium carrots), peeled, halved lengthwise, and cut into 1/2-inch thick slices, divided; 3 tablespoons (45ml) extra-virgin olive oil, divided; Kosher salt; 1 large leek (10 1/2 ounces; 300g), white and pale green parts only, thinly sliced; 1 large yellow onion (12 ounces; 340g), thinly sliced; 2 medium garlic cloves, peeled and smashed under the flat side of a knife; 3 sprigs flat-leaf parsley; 5 cups (1.2L) homemade or store-bought vegetable stock, plus more as needed; 1 cup (235ml) fresh or store-bought carrot juice, plus more as needed; 4 tablespoons unsalted butter (2 ounces; 60g), divided