Melt butter over medium heat in a Dutch oven or medium heavy-bottomed pot. Add carrots, potato, onion, and celery. Sauté, stirring occasionally, until onion and celery have softened, about 3 minutes. Stir in the garlic until fragrant, about 20 seconds.
Add in the vegetable broth, brown sugar, ginger, and thyme. Bring to a boil, then reduce heat to a gentle bubble. Cover and simmer, stirring occasionally, until vegetables are tender, about 30 minutes. Uncover and reduce the heat to low to cool down for 15 minutes.
Using a handheld immersion blender, blend soup in the pot until smooth (alternatively, carefully transfer the soup to a blender in batches and blend until smooth, then add back to the pot.)
Stir in the heavy cream, curry powder, salt, and pepper.
Continue cooking on low heat for about 5 more minutes just to warm through.
Ladle into bowls with a drizzle of cream, a crank of fresh cracked black pepper, and a sprig of fresh thyme for garnish.
