Preheat the oven to 375°F (190°C).
Steam or blanch the broccoli until tender but bright green, about 3-5 minutes. Drain and set aside.
In a large skillet, warm the olive oil over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.
Stir in the shredded chicken and cooked broccoli. Add salt, pepper, and Italian seasoning, stirring thoroughly to blend the flavors.
In a medium bowl, mix together the ricotta cheese, egg, and half of the grated mozzarella.
In a greased 9x13-inch baking dish, spread a thin layer of the chicken and broccoli mixture on the bottom.
Place three sheets of lasagna noodles on top of the chicken mixture.
Spoon a layer of the ricotta cheese mixture over the noodles, smoothing it out evenly.
Repeat layering with chicken and broccoli mixture, noodles, and cheese mixture until all ingredients are used, finishing with a layer of chicken and broccoli on top.
Top with the remaining mozzarella cheese and grated Parmesan.
Cover with aluminum foil and bake for 30 minutes. Remove foil and bake for an additional 15 minutes or until the cheese is bubbly and golden brown.
Allow the lasagna to cool for 10-15 minutes before slicing and serving.