Place finely chopped hard-boiled eggs into a medium-sized stainless steel mixing bowl.
Add the shredded mozzarella, mayonnaise, sriracha, and minced chives to the eggs.
Season the mixture with salt and black pepper; fold gently with a spatula until the binder is evenly distributed and the mixture holds together when pressed.
Preheat a heavy-bottomed non-stick skillet over medium-high heat until a drop of water sizzles immediately.
Apply a light coating of olive oil spray to the skillet surface.
Using a 1/4 cup measuring scoop, portion the egg salad mixture into the skillet, leaving 2 inches between each portion.
Flatten each portion slightly with a metal spatula into a disc approximately 1/2-inch thick.
Sear undisturbed for 2 minutes or until the cheese melts and forms a deep golden-brown crust.
Carefully flip each patty using a thin-edged spatula and sear the reverse side for an additional 60-90 seconds.
Transfer the crispy egg salad patties immediately to toasted sourdough or avocado-spread crackers and serve warm.