Mix first five ingredients in the bowl of a food processor. Pulse until broccoli and artichoke hearts evenly mixed with the cheese.
Continue to mix until eggs are well-incorporated. Transfer mixture to a medium mixing bowl.
Mix in 1 cup of the mozzarella and red pepper flakes, if desired.
Transfer mixture to an 8 x 8 x 2 inch baking dish. Sprinkle remaining mozzarella cheese over the top.
Bake for 20-25 minutes until dip is hot and bubbly and the top starts to turn golden brown.