Combine cream and eggs in large bowl, mixing well; add cayenne pepper. Coat bottom and sides of hotel pan with butter. Arrange rutabagas in bottom of pan; season with salt and black pepper. Top with 8 oz cream mixture. Repeat layers with remaining vegetables and cream mixture, seasoning each vegetable layer with salt and black pepper.
Bake, covered, in 375°F oven 1 hour or until vegetables are just tender. Uncover; sprinkle cheese evenly over top. Continue baking, uncovered, until cheese is lightly browned. Cool slightly. Cut into 4 x 4-inch portions. Keep warm; set aside.