Position an oven rack in the middle and preheat the oven to 375°F (190°C).
Make the sauce: Heat olive oil in a medium saucepan over medium heat and sauté the chopped onion until soft and translucent, about 5 minutes.
Add the minced garlic, red pepper flakes, Italian spice mix, and tomato paste; sauté 1 minute until fragrant.
Stir in the crushed tomatoes, bring to a simmer, and cook gently for about 20 minutes; season with salt and pepper to taste.
Prepare the filling: Reserve 1 cup of the shredded cheese for topping later.
In a large bowl, combine the ricotta, remaining shredded cheese (about 3 cups), beaten egg, 1/2 teaspoon salt, 1/2 teaspoon pepper, and the chopped spinach until evenly mixed.
Soak the no-boil lasagna noodles in hot water for about 5 minutes to soften, then drain and lay them on a clean kitchen towel to remove excess water.
Spread half of the sauce over the bottom of a 9 x 13-inch baking dish.
Assemble the manicotti: Place about 1/4 cup of the cheese and spinach mixture along the short side of each noodle and roll up the noodle tightly; place seam-side down in the prepared dish over the sauce.
Pour the remaining sauce over the rolled noodles, cover the dish with foil, and bake for 40 minutes.
Remove the foil, sprinkle the reserved 1 cup shredded cheese evenly over the top, and bake uncovered about 5 more minutes until the cheese is melted.
Let the casserole rest about 10 minutes before serving.
