Preheat the oven to 350°F (175°C) and lightly spray a 9x13-inch baking dish with nonstick cooking spray; set aside.
Bring about 3 quarts of water to a boil in a large pot and cook the lasagna noodles until just tender, about 6–8 minutes; drain and lay the noodles flat on a cutting board or clean surface.
In a mixing bowl, combine the chopped artichoke hearts, spinach (or thawed, well-drained frozen spinach), shredded chicken if using, mayonnaise (or Greek yogurt), grated Parmesan, grated Monterey Jack, garlic powder, and kosher salt; stir until evenly mixed.
Spoon and spread a portion of the spinach-artichoke mixture evenly over each lasagna noodle, leaving a small border at the edges.
Starting at one end, roll each filled noodle into a tight roll and place seam-side down in the prepared baking dish, arranging rolls in a single layer.
Spread any remaining filling over the tops of the rolls and bake until heated through and the cheese is melted, about 20 minutes.