Cut jalapeños in half, and remove stems and seeds.
Place jalapeño halves on a foil-lined sheet pan and broil for 3-5 minutes, or until the peppers are blackened. Set aside to cool.
Preheat oven to 375 degrees.
Drain artichoke hearts and pat dry, then chop into very small pieces. Place into a large bowl.
Open can of green chiles and drain any excess liquid, then add to the bowl with the artichoke hearts.
Chop cooled jalapeños and add to bowl.
Add cheddar cheese, mozzarella cheese, cream cheese, 1.5 tablespoons of the parmesan cheese, mayonnaise, and garlic powder, and stir well.
Spread dip into an 8-inch baking dish, then sprinkle the top with the rest of the parmesan cheese and then the paprika.
Bake for 20-30 minutes, until dip is bubbly and the top is lightly browned.
Remove from oven, let cool for 5 minutes on cooling rack, then serve.
Notes
Make-Ahead Instructions: Prep all the ingredients, add to baking dish, then cover and chill for up to 24 hours. Remove from the refrigerator about 30 minutes before baking to allow dish to come back to room temperature. Then bake and serve. Freezing this dip is not recommended! Expert Tips: Make sure that you chop your jalapeños very finely after they are broiled to avoid getting a mouthful of straight jalapeño when the dip is served. Also, you may want to use disposable kitchen gloves when chopping and de-seeding.