Cake:
Nonstick cooking spray, for the baking sheets and parchment
Three 15.25-ounce boxes of white cake mix, such as Duncan Hines
Three 3.4-ounce packages of instant vanilla pudding mix
1 1/2 cups vegetable oil
12 large egg whites
Forest green gel food coloring, for coloring the batter
Frosting:
1 cup plus 2 tablespoons sugar
1 tablespoon lemon juice
Pinch fine salt
6 large egg whites
4 1/2 sticks (18 ounces) unsalted butter, at room temperature, cut into 1 1/2-inch chunks
1 1/2 teaspoons pure vanilla extract
Leaf green gel food coloring, for coloring the frosting
Decorations:
3 tablespoons desiccated coconut
White nonpareils, for dusting
18 white gumdrops
36 candy-coated chocolates with almonds or peanuts, such as M and M's
Star Topper:
Nonstick cooking spray, for the parchment and cookie cutter
2 clear mint candies, crushed
Special equipment:
three 18-by-13 rimmed baking sheets; a large cake board or cutting board; a ruler; a piping bag fitted with a small fluted tip; a 2-inch metal star cookie cutter; a birthday candle; a long wooden skewer; an offset spatula