Place the eggs in a pot and cover with cold water. Bring to a boil over medium heat, then remove from heat, cover, and let sit for 12 minutes.

Drain the hot water and cool the eggs under cold running water. Peel the eggs and slice each one in half lengthwise.

Scoop the yolks into a mixing bowl. Add the mayonnaise, mustard, salt, and black pepper. Mash and stir until the mixture is smooth.

Spoon most of the yolk mixture back into the egg white halves, filling them evenly.

Mix the black food coloring into the remaining yolk mixture until it turns dark. Transfer this dark mixture to a small piping bag or zip-top bag with a tiny corner snipped off.

Pipe thin concentric circles on top of each filled egg. Use a toothpick to drag lines from the center outward, creating a web pattern on each one.