Layers of carrot flavor define this spicy soup: Carrot peels are simmered in stock, cut-up carrots are sweated to extract their essence, and carrot juice is added as a final touch.
Heat stock, carrot peels, and carrot trimmings in a medium saucepan over low heat 15 minutes. Pour stock through a fine sieve into a bowl; discard solids.
Heat 2 tablespoons butter and the oil in a medium saucepan over medium-high heat. Add shallot and carrots; cook until slightly softened, about 5 minutes.
Stir in curry powder; cook 30 seconds. Add stock; bring to a boil. Reduce heat to medium-low; simmer until carrots are tender, about 10 minutes. Season with salt. Remove from heat; let cool slightly.
Meanwhile, bring 1 1/4 cups water to a boil in a small saucepan. Add couscous and 1/2 teaspoon salt. Cover; return to a boil. Reduce heat to low; cook 6 minutes. Remove from heat; let stand 5 minutes.
Working in small batches, process soup in a food processor until smooth. Transfer to a clean saucepan. Add carrot juice. Heat over medium-low heat until warm (do not let boil). Season with salt.
Melt remaining 2 tablespoons butter in a medium saute pan over low heat. Stir in couscous to coat; cook just until warmed through. Divide couscous among serving bowls; ladle in soup. Garnish with cilantro. Serve with limes.