In a large pot of boiling water, cook the carrots until very tender (about an hour). Drain, and transfer to a large mixing bowl.
While carrots are warm, mix together the carrots, sugar, baking powder, and vanilla until smooth. Mix in the flour, eggs, and butter. Transfer to a 2qt baking dish.
Bake 1 hour or until top is golden brown. Sprinkle top with powdered sugar.