Preheat oven to 350°F. Grease an 8-inch square baking dish.

Place carrots in saucepan and cover with salted water. Bring to a boil, then reduce heat and simmer, uncovered, for 20 minutes or until carrots are tender. Drain and set aside.

In a blender or food processor, combine eggs, butter, sugar, flour, baking powder, and vanilla. Add carrots a little at a time and puree.

Pour mixture into prepared baking dish. Bake for 45 minutes, or until firm.

Let stand for 5 minutes before serving.

Note: This may be made a day ahead and refrigerated. Bring to room temperature before cooking.