Add the spinach to a food processor fitted with the blade attachment and pulse until finely chopped.
Heat a medium heavy bottomed pot over medium heat, add the olive oil and heat through. Add the onions and sauté, stirring occasionally, until they are soft and translucent, about 4 minutes. Add the garlic and sauté until fragrant, about 30 seconds.
Stir in the red pepper flakes and balsamic vinegar followed by the artichokes and spinach. Season with salt.
Stir in the heavy cream followed by the cream cheese. Continue to stir, cooking over medium heat until the cream cheese blends and the mixture is creamy, about 2 minutes.
Add the mozzarella, Asiago, Parmesan and Pecorino cheeses, stirring to combine. Lower heat to medium-low and continue to cook until the cheese has completely melted, about an additional 2 minutes.
Serve hot with bread, chips, or vegetables for dipping.
Video
Notes
Drain the spinach thoroughly before adding it to the dip to prevent excess moisture and ensure a thick, creamy consistency.