In a large pot, heat 1/4 cup of the oil. Add the onion and cook over moderately high heat, stirring frequently, until softened, about 6 minutes. Add the garlic, ginger and curry powder and cook, stirring, until fragrant, about 2 minutes. Add the carrots and cook, stirring, for 2 minutes longer. Add the water and sugar and season with salt and pepper. Simmer over moderately low heat until the carrots are very tender, about 45 minutes.
Meanwhile, in a small saucepan of boiling salted water, blanch the tarragon and parsley just until wilted, about 30 seconds. Drain the herbs and transfer to a bowl of ice water, then drain again, squeezing out the excess water. Transfer to a blender. Add the remaining 1/2 cup of olive oil and puree until smooth. Strain the oil through a double layer of cheesecloth without pressing down on the solids.
Carefully puree the hot soup in a blender or food processor until smooth. Return the soup to the pot, stir in the lemon zest and season with Tabasco and salt and pepper. Ladle the soup into shallow bowls, drizzle with the tarragon oil and garnish with chives.