Preheat the oven to 350 degrees F. Line the bottom of a 9-by-13-inch baking pan with parchment paper and spray with nonstick spray.
Whisk the flour, granulated sugar, brown sugar, cocoa powder, baking soda, salt and baking powder together in a large bowl. Add the eggs, milk, coconut oil, vinegar and vanilla. Beat with an electric mixer at medium speed until smooth, about 2 minutes. Beat in the hot water until smooth.
Pour the batter into the prepared pan and tap against the counter to remove any air bubbles. Bake until a toothpick inserted into the center of the cake comes out clean, about 35 minutes. Let cool completely in the pan. Invert onto a serving platter or cutting board.
Spread the frosting evenly over the cake. Sprinkle evenly with the crushed chocolate graham crackers.
Microwave the marshmallows in a microwave-safe medium bowl until they puff and are soft enough to stir, about 1 minute. Stir in about a 1/4 teaspoon yellow food coloring and 1/4 teaspoon green food coloring.
Using two forks, pick up a tablespoon-sized blob of the melted marshmallow and stretch it over and around the cake; repeat so that the strings of marshmallow crisscross one another in all directions. Continue until you have what looks like a spiderweb. You can spray your hands with cooking spray and arrange strands once the marshmallow is cool enough to handle. Microwave the mixture for 30 seconds to loosen up as needed.
Decorate the top of the cake with gummy candies and sprinkles.