Preheat the oven to 375°F. Bring a large pot of salted water to a boil. Cook the shells, stirring occasionally to prevent sticking, until al dente, about 3 minutes less than the package instructions. Drain well and run under cold water to prevent further cooking. Drain again.
In a large bowl, lightly whisk the eggs. Stir in the ricotta, spinach, parmesan, parsley, and 1½ cups mozzarella. Season with ¼ teaspoon salt and pepper to taste. Transfer the filling to a gallon-size freezer bag.
Spread 1½ cups marinara sauce in a 9x13 baking dish. Snip off a corner of the bag with the filling and squeeze the filling into the shells, arranging 20-24 filled shells in the baking dish in a single layer. Top with the remaining marinara sauce and mozzarella cheese.
Cover the pan tightly with foil. Bake until heated through and bubbling on the edges, 40 minutes. Uncover and continue baking about 10 minutes more, until the sauce is bubbling and the cheese has fully melted.
Let stand 5-10 minutes before serving. Sprinkle with additional parmesan cheese before serving, if desired.
To refrigerate and serve later: Before baking, the dish can be prepared up to 5 days in advance and refrigerated. Bake from the fridge, covered at 375°F for 40-45 minutes, until heated through.To freeze and serve later: Before baking, the dish can be prepared in a freezer-to-ovenproof baking dish, covered tightly, and frozen for up to 3 months. Bake from frozen (no need to thaw) at 375°F, covered, until heated through in the center, and bubbling on the edges, about 1 hour. Uncover and bake until any liquid on the edges dries up, 15-20 minutes more.