Preheat your oven to 375°F (190°C).
In a medium saucepan, heat the olive oil over medium heat and sauté the minced garlic until fragrant, about 1 minute.
Add the shredded chicken and fresh spinach to the saucepan, stirring until the spinach wilts. Season with salt, pepper, oregano, and basil. Mix well and remove from heat.
In a mixing bowl, combine the ricotta cheese and 1 cup of the shredded mozzarella cheese. Set aside.
Cook the gluten-free lasagna noodles according to package instructions, then drain and layer them on a flat surface.
Spread a thin layer of chicken broth on the bottom of the baking dish.
Lay 3 lasagna noodles on top of the broth. Spread half of the chicken and spinach mixture over the noodles, followed by half of the ricotta and mozzarella mixture.
Repeat this layering process with another set of 3 noodles, the remaining chicken and spinach mixture, and then the remaining cheese mixture.
Finish with a layer of 3 lasagna noodles on top and pour the remaining chicken broth over the top. Sprinkle the remaining mozzarella and all of the grated Parmesan cheese on the top layer.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 20 minutes, or until the cheese is golden and bubbly.
Allow the lasagna to cool for about 10 minutes before slicing and serving.