Prep: Preheat oven to 425°F. You'll need a rimmed baking sheet. You can line with parchment or a silicone mat for easy cleanup, but it isn't required.
Prep the carrots: It isn't necessary to peel the carrots for this recipe, but make sure that you give them a good scrub to remove any dirt. Pat them dry, trim off the ends, and chop into roughly 1" pieces.
Season and roast carrots: Transfer the carrots to the baking sheet. Drizzle with 2 tablespoons olive oil, season with salt and pepper, and toss with your hands to coat. Spread the carrots out into an even layer and roast for 35-40 minutes, until tender and lightly caramelized. You can give them a toss at the 20 minute mark to help them cook evenly.
Sauté aromatics: While the carrots roast, heat 1 tablespoon olive oil in a pot over medium heat. When oil shimmers, add diced onion, diced jalapeños or serranos, minced garlic, and minced or grated ginger. Sauté until translucent, about 4-6 minutes. Add in turmeric and black pepper, stir to coat the veggies, and sauté for another 30-60 seconds.
Add liquids: Pour in 4 cups of vegetable broth and the canned coconut milk. Stir and allow the mixture to come up to a boil. Reduce heat to low, cover partially, and allow the soup to gently simmer for 10-15 minutes, or until the carrots are done roasting.
Add roasted carrots and blend: Once the carrots are roasted, scoop them into the soup. Use an immersion blender to purée the soup till smooth. If you prefer a thinner soup, blend in additional vegetable broth to taste. (If you don't have an immersion blender, transfer the roasted carrots directly to a blender. Ladle about 2 cups of the broth into the blender with the carrots and carefully blend till smooth. Stir the puréed mixture back into the soup pot. Check the notes for important Safety Tips for Blending Hot Liquids.)
Taste and adjust: Stir in fresh lime juice. Taste the soup and adjust salt, pepper, and acidity to preference.