Preheat the oven to 350°F (175°C) and spray a 9×13 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 drained chopped artichoke hearts, spinach (fresh or thawed/drained frozen), shredded chicken if using, mayonnaise (or Greek yogurt), grated Parmesan, grated Monterey Jack, garlic powder, and kosher salt; stir until evenly mixed.
Spread a portion of the spinach–artichoke mixture evenly over each lasagna noodle, leaving a small border at the edges.
Starting at one short end, roll each noodle up tightly to enclose the filling and place seam-side down in the prepared baking dish.
Spread any remaining filling over the tops of the rolls, then bake until heated through and the cheese is melted, about 20 minutes.
