Preheat the oven to 375°F (190°C) and spray a 2-quart casserole dish or a 9-inch high-sided pie plate with cooking spray; set aside.
In a large mixing bowl, combine the softened cream cheese, sour cream (use 1/3 cup to start and up to 1/2 cup if you prefer it creamier), mayonnaise, and minced garlic.
Beat the mixture with a handheld electric mixer on high until smooth and well combined.
Stir in 1 cup of the shredded mozzarella, 1/2 cup of the grated Parmesan, kosher salt, and black pepper until evenly distributed.
Fold in the drained, quartered artichoke hearts and the well-squeezed thawed spinach (use the larger amount of spinach if you want it more noticeable).
Transfer the mixture to the prepared baking dish and smooth the top. Evenly sprinkle with the remaining 1/2 cup mozzarella and 1/4 cup Parmesan.
Bake for about 30 minutes, checking at 20 minutes; bake until the dip is bubbly and the top is golden to your liking (it may take up to ~35 minutes depending on your oven).
Remove from the oven and serve immediately.