For the Lemon-Herb Yogurt: In a small bowl, whisk together Greek yogurt, lemon juice, and parsley until well combined. Cover and refrigerate.

For the Carrot Soup: Adjust oven rack to middle position and preheat to 375°F (190°C). On a parchment-lined rimmed baking sheet, toss half of the carrots (1 ¼ pounds) with 1 tablespoon (15ml) oil; season with salt. Roast, stirring halfway through, until carrots are tender and deep golden brown in spots, about 25 minutes. Set aside.

In a large Dutch oven or pot, heat remaining 2 tablespoons (30ml) oil over medium heat until shimmering. Add leek, onion, and garlic, and cook, stirring frequently, until softened but not browned, 7 to 10 minutes.

Add remaining carrots along with the roasted carrots, parsley sprigs, vegetable stock, and carrot juice. Season lightly with salt. Bring to a boil over high heat, then lower to maintain a steady simmer. Cook, stirring occasionally, until all the carrots are completely tender, about 25 minutes. Discard parsley.

Ladle half of liquid and solid ingredients into a blender jar and add half of the butter (1 ounce; 2 tablespoons). Remove the blender lid plug (this will allow steam pressure to escape), close lid, and set a folded clean dish towel on top to cover the hole in the blender lid (keep your hand on the towel to hold it in place). Starting at the lowest speed and gradually increasing to the highest, blend the soup until it is completely smooth. Transfer soup to a large pot (if an even smoother texture is desired, pass soup base through a fine-mesh strainer into the pot). Repeat with remaining soup and butter. If soup is too thick, thin as needed with additional vegetable stock or carrot juice to desired consistency (the consistency should not be a thick purée, but rather a silky, creamy, soup-like one). Whisk in lemon juice and season to taste with salt.

Divide soup among warmed bowls and drizzle with lemon-herb yogurt.