Preheat the oven to 350°F (175°C). Spread about 1 cup of marinara sauce evenly across the bottom of a 9 x 12 inch baking dish.
Cook the lasagna noodles according to package directions until al dente, then drain in a colander and lay noodles flat on a work surface or clean towel.
In a medium bowl, combine the squeezed spinach, chopped artichoke hearts, ricotta, grated Parmesan, minced garlic, large egg, 1/2 teaspoon kosher salt, and a few grinds of black pepper; stir until evenly mixed.
Working with one noodle at a time, spread about 1/3 cup of the spinach–artichoke filling in an even layer over the noodle, leaving a small border at the edges. Roll the noodle tightly from one end to the other and place seam-side down in the prepared baking dish. Repeat with remaining noodles and filling.
Spoon the remaining marinara sauce over the assembled roll-ups and sprinkle approximately 1 tablespoon shredded mozzarella on top of each roll.
Cover the dish with foil and bake for 40 minutes, until heated through and the cheeses have melted. Remove foil for the last few minutes if you want the tops slightly browned.
To serve, spoon additional marinara on plates if desired and place roll-ups on top. Garnish with chopped parsley, if using.