Lightly grease an 8x4-in. loaf pan. Line with parchment and grease the paper; set aside. In a skillet, saute the carrots in butter until tender; cool slightly. , Transfer to a food processor; cover and process until pureed. Add the egg, egg yolk, cream, sugar, nutmeg and allspice. Cover and process until well combined; set aside., For broccoli layer, place 1 in. of water in a small saucepan; add broccoli. Bring to a boil. Reduce heat; cover and simmer for 7-9 minutes or until tender. Drain; cool slightly. , Transfer to a food processor; cover and process until pureed. Add the egg, butter, cream, nutmeg and salt. Cover and process until well combined; set aside., For potato layer, in a skillet, saute potatoes and onion in butter until tender; cool slightly. Transfer to a food processor; cover and process until pureed. Add the remaining ingredients. Cover and process until well combined., Spread carrot mixture evenly in the prepared pan. Top with broccoli and potato layers. Place pan in a larger baking pan. Fill larger pan with boiling water to a depth of 1 in. , Bake, uncovered, at 350° for 50-60 minutes or until a thermometer reads 160°. Let stand for 10 minutes before inverting onto a serving platter; remove parchment. With a sharp knife, cut into slices.