Prepare the Oven: Preheat the oven to 400°F and line a large rimmed baking sheet with parchment paper if desired for easier cleanup.
Prepare the Carrots: Peel the carrots, then cut them diagonally into pieces about ½ inch thick at the widest part so they roast evenly.
Season the Carrots: Place the carrots on the prepared baking sheet, add 2 tablespoons of the olive oil and ½ teaspoon of the salt, then toss until the pieces are lightly coated and seasoned.
Arrange for Roasting: Spread the seasoned carrots across the baking sheet in a single layer so they roast evenly.
Roast the Carrots: Roast for 25 to 40 minutes, tossing halfway through, until the carrots are caramelized around the edges and easily pierced with a fork; heirloom carrots may take about 25 minutes, while regular carrots generally need 35 to 40 minutes.
Cook the Onion: When the carrots are nearly finished, heat the remaining 1 tablespoon olive oil in a Dutch oven or soup pot over medium heat until shimmering, then add the chopped onion and ¼ teaspoon salt. Cook for 5 to 7 minutes, stirring occasionally, until the onion softens and becomes translucent. Add the Aromatics: Stir in the garlic, ground coriander, and ground cumin, cooking for about 30 seconds to 1 minute while stirring constantly, until fragrant.
Add the Liquids: Pour in the vegetable broth and water, using a wooden spoon or sturdy silicone spatula to scrape up any browned bits from the bottom of the pot.
Combine the Carrots: Add the roasted carrots to the pot once they come out of the oven, then bring the soup to a boil over high heat.
Simmer the Soup: Reduce the heat as needed to maintain a gentle simmer and cook for 15 minutes, allowing the flavors to meld.
Cool Before Blending: Remove the pot from the heat and let the soup cool for a few minutes before transferring it to the blender.
Blend Safely: Carefully transfer the soup to a blender in batches if necessary, making sure not to fill the blender beyond its maximum fill line to prevent the hot soup from overflowing.
Finish the Soup: Add the butter, lemon juice, and several twists of freshly ground black pepper, then blend until completely smooth.
Adjust the Flavor: Taste the soup and add more salt or pepper as needed; blend in another tablespoon of butter for additional richness or a little more lemon juice for extra brightness.
Serve: Serve the soup once it has been blended smooth and seasoned to taste.
Store: Keep the covered soup refrigerated for about four days, or freeze it for several months.