Bring a large pot of water to boiling. Add all the spinach and blanch for about 3-4 minutes. The spinach should be a rich green color. Drain into a colander and rinse with cold water. Using your hands, form the spinach into a ball and squeeze as much of the liquid out as possible. Place the spinach on several layers of paper towels and wrap. Twist the paper towels so they absorb more of the remaining liquid. You can use a clean kitchen towel instead of paper towels for this step. Once you've removed as much of the liquid as you can, unwrap and place on a cutting board. Chop into small pieces and set aside until needed.

Preheat oven to 425 degrees.

In a 2 qt. saucepan, melt 2 T of butter and add the onion. Sprinkle a dash of salt over the onions to help them sweat (soften). Sauté over med-low heat until translucent, about 5-8 mins.

Add the garlic and sauté another 1-2 minutes until fragrant.

Stir in the artichokes and chopped spinach until combined.

Add the cream cheese, and Monterey Jack, and parmesan cheeses and continue to cook the mixture until the cheese has melted and blended in. At this point it's going to be pretty lumpy and thick.

Add 1 C of heavy cream and stir until combined. It will still be on the thicker side. Slowly add more cream until the dip is smooth and creamy or until you get the consistency you like.
Hint: If you want to serve this with thinner chips, you definately will want to add more cream.

Stir in the remaining 2 T of butter. (This adds a velvety, rich texture to the dip but can be omitted if desired).

Pour the mixture into an ovenproof deep dish and bake until nice and bubbly, about 10 minutes. Sprinkle with more parmesan and serve while hot.