Preheat the oven to 350°F (175°C) and spread about 1 cup of marinara sauce on the bottom of a 9 x 13-inch baking dish.
Cook the lasagna noodles according to package directions until al dente, then drain and lay them flat on a work surface.
In a medium bowl, combine the squeezed spinach, chopped artichoke hearts, ricotta, grated Parmesan, minced garlic, 1 large egg, 1/2 teaspoon kosher salt, and black pepper; mix until evenly incorporated.
Spoon about 1/3 cup of the spinach–artichoke filling onto each noodle and spread it into an even layer, leaving a small margin at the edges.
Roll each noodle tightly and place seam-side down in the prepared baking dish. Repeat with remaining noodles and filling to make 8 rolls.
Ladle the remaining marinara sauce evenly over the rolls and sprinkle about 1 tablespoon of shredded mozzarella on top of each roll.
Cover the dish with foil and bake for 40 minutes, until the rolls are heated through and the cheese has melted; remove foil for the last few minutes if you want the cheese browned.
To serve, spoon additional marinara sauce onto plates, place roll-ups on top, and garnish with chopped parsley if desired.