Preheat oven to 375°F. Spray a 12-inch oven safe skillet or 2 quart casserole dish with nonstick cooking spray; set aside.
Toss together shredded mozzarella and shredded cheddar cheese. Set aside one cup for the top. (The rest goes into the dip mixture.)
In a large bowl, use an electric mixer to whip together plain cream cheese, chive and onion cream cheese, sour cream, heavy cream, sundried tomato pesto, calabrian chile paste (or red pepper flakes to taste) rosemary, Italian seasoning, salt and black pepper until smooth.
To the bowl stir in chicken, chopped sundried tomatoes, and 2 1/2 cups of the cheese mixture until incorporated.
Spoon the creamy chicken dip mixture into the prepared skillet or dish and top with the reserved one cup shredded cheese blend.
Lightly spray a piece of aluminum foil with cooking spray. Place foil, cooking spray-side down, over chicken dip mixture. Bake in preheated oven for 25 minutes.
Remove foil and top with grated Parmigiano-Reggiano or Parmesan cheese. Bake, uncovered, for another 10-15 minutes until bubbly and the cheese is golden brown. (You can turn the oven to broil at the end of baking to brown the top.)
Garnish with chopped fresh parsley or fresh basil leaves and serve immediately with crostini, pita chips, crackers, baguette slices or garlic bread for dipping.