Preheat the oven to 200°F/93°C and line a large baking sheet with parchment paper or a silicone mat. Set aside.
Before you whip up the meringue, make sure there are no traces of grease on the whisk attachment or in your bowl. Grease can prevent the meringue from whipping up properly. If you see or feel any grease, moisten a paper towel with vinegar and wipe the inside of the bowl and the whisk attachment to remove any grease.
Then add 4 large, room-temperature egg whites into the bowl of a stand mixer with a whisk attachment and mix on medium speed until the surface of the egg whites is covered in small bubbles. Add 1/4 tsp cream of tartar and continue to mix until it reaches the soft peak stage and leaves visible tracks.
Gradually mix 1 cup of granulated sugar, 1 Tbsp at a time, into the egg whites over a few minutes while mixing on a medium-low speed. Adding the sugar gradually makes a huge difference in the stability of the meringue. Increase the mixing speed to a medium-high speed (6 on a KitchenAid). When the meringue gets close to reaching stiff peaks, add 1/2 tsp of vanilla or almond extract. Keep mixing until stiff, glossy peaks form.
Scoop about a third of the meringue into a separate bowl and color it green with a generous squirt of gel food coloring. Mix just until it's evenly colored, then scoop it into a small piping bag fitted with a large round piping tip (like a Wilton 1A). If you don't have one that size, cut an opening at the base of the bag that's 3/4 inch wide. Seal the top of the bag with a clip or rubber band and set aside.
Repeat the prior step to make neon purple and orange meringue. Scoop each color into its own piping bag.
Pipe dollops of meringue on the prepared pans. I layered some of the dollops to make the monsters different heights. You can get creative with this part and make each monster unique. These don't spread as they bake, so they can be piped about 1 inch apart.
Bake the tray on the middle rack of your oven for 2 hours, then turn the oven off and let the meringue sit in the oven for another hour. Letting them gradually cool helps prevent them from cracking. At this point, the meringue should be fully cooked and look and feel dry to the touch. If they still seem wet or moist, leave them in the oven for another hour.
Remove the tray from the oven. They should have a crunchy exterior and a soft, chewy center. Let the meringues cool fully to room temperature, then add candy eyes onto each meringue with a bit of melted white chocolate (I added 1-3 eyes per meringue). These can be stored at room temperature for up to two weeks.