Bring a large pot of salted water to a boil. Add the lasagna noodles and cook according to the package instructions until al dente. Drain and lay them flat on a clean kitchen towel to prevent sticking.
Heat a skillet over medium heat. Add a splash of olive oil, then sauté the minced garlic until fragrant, about 30 seconds. Add the fresh spinach and cook until just wilted, about 2-3 minutes. Remove from heat and squeeze out any excess moisture from the spinach. Chop roughly.
In a mixing bowl, combine the shredded chicken, wilted spinach, ricotta cheese, half of the mozzarella, Parmesan cheese, Italian seasoning, salt, and pepper. Stir until everything is well incorporated.
Preheat your oven to 375°F (190°C). Lightly grease your baking dish with olive oil. Spread about 1/2 cup of marinara sauce evenly across the bottom of the dish. Lay one lasagna noodle flat and spread a generous layer of the chicken and spinach filling evenly over the noodle. Roll the noodle up from one end to the other. Place the roll seam side down in the baking dish. Repeat with the remaining noodles and filling.
Pour the remaining marinara sauce over the top of the roll-ups. Sprinkle the remaining mozzarella cheese evenly on top.
Cover the baking dish with foil and bake for 25 minutes. Remove the foil and bake for an additional 10 minutes, or until the cheese is bubbly and golden. Let the roll-ups cool for a few minutes before serving.