Slice cake into 3 equal layers; it's easier when frozen. Cut two 3-3/4-inch rounds from each layer. Top layer is bun top, middle layer is meat patty, and bottom layer is bun bottom.
Cut trimmings in 1/2-inch-wide pieces for "fries." Toast fries in toaster oven until lightly browned. Sprinkle with sugar.
For meat patty, frost round middle cake pieces with chocolate frosting.
Spread white frosting ("mayo") over bottom cake buns, meat and underside of top cake buns. Tint coconut green for "lettuce" and sprinkle on "meat." Top with fruit roll-up "tomato" pieces. Or spread with "ketchup" (white frosting tinted red). Spread top with softened honey; sprinkle with seeds. Assemble burgers and serve with fries on plate with a puddle of "ketchup."