Preheat the oven to 475 degrees F.
Put the carrots in a medium bowl, drizzle 1 tablespoon of the olive oil over, season with a good pinch each of salt and pepper, and toss to evenly coat. Scatter the carrots on a rimmed baking sheet and roast in the oven until lightly caramelized and aromatic, about 20 minutes.
In a heavy pot, heat the remaining 2 tablespoons of the olive oil with the butter over medium heat until the butter is melted. Add the onion and celery and cook, stirring occasionally, until translucent and tender, about 5 to 7 minutes. Add the carrots, garlic, ginger, and a good pinch of salt, then pour in the water and bring just to a boil. Reduce the heat to medium-low and simmer until the carrots are fully tender, about 15 minutes. Take the pot from the heat and let cool.
When the soup has cooled, purée it in batches in a food processor or blender. Return the purée to the pot, stir in the heavy cream, and reheat for a few minutes. Taste, adding more salt or pepper if needed. Spoon the soup into bowls, drizzle the honey over, add a sprinkle of chives, and serve.