Preheat the oven to 400 degrees F and lightly coat a 1 1/2-quart baking dish with cooking spray.
Blend the cottage cheese and Greek yogurt in a food processor for 1 to 2 minutes, until smooth and creamy. Scrape the mixture into a large bowl.
Stir 3/4 cup mozzarella, 1/4 cup Parmesan, spinach, artichoke hearts, garlic, lemon juice, onion powder, salt, crushed red pepper, and black pepper into the cottage cheese mixture.
Spread the dip evenly in the prepared baking dish. Top it with the remaining mozzarella and Parmesan.
Bake for 22 to 26 minutes, until the edges are bubbling and the center is hot. Broil for 1 to 2 minutes to brown the cheese, watching it closely.
Let the dip rest for 5 minutes so it thickens slightly. Sprinkle with green onions and serve warm with toasted bread, pita wedges, or crisp vegetables.