01 - Place eggs in a saucepan and cover by at least one inch with water. Bring to a boil over medium-high heat, reduce heat, and simmer gently for 10 minutes.
02 - Transfer cooked eggs to a bowl of cold water. Once cool enough to handle, gently tap the shells all over to create cracks without removing the shells.
03 - In a clean saucepan, combine 4 cups water, black tea leaves or tea bags, salt, and black food coloring. Bring to a low simmer.
04 - Place the cracked eggs into the colored tea mixture. Simmer for 10 minutes, then remove from heat and let soak an additional 15 to 20 minutes to intensify the pattern.
05 - Remove eggs from the dye bath. Peel off the shells to reveal the spiderweb design, then slice eggs in half lengthwise.
06 - Gently remove yolks from each egg half and place in a mixing bowl. Mash yolks thoroughly with mayonnaise, Dijon mustard, vinegar, and finely ground black sesame until creamy. Season with salt and black pepper to taste.
07 - Pipe or spoon the prepared filling into the hollows of each egg white half.
08 - Sprinkle each deviled egg with whole black sesame seeds for garnish before serving.