Heat a large skillet over medium heat. Add pine nuts and cook, stirring occasionally, until toasted and fragrant, about 3 minutes. Transfer to a food processor.

Place basil leaves, 3/4 cup Parmesan cheese, 1/2 cup olive oil, and 4 cloves garlic in the food processor with the pine nuts. Blend pesto into a smooth paste, about 3 minutes.

Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in the boiling water, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain.

Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch casserole dish with cooking spray.

Heat 3 tablespoons oil in a large skillet over medium-high heat. Add onion and 3 cloves garlic; cook and stir until translucent, about 5 minutes. Add spinach; cook and stir until heated through, about 5 minutes. Stir in chicken; cook until heated through, about 5 minutes. Season with salt and black pepper.

Mix ricotta cheese, 3/4 cup Parmesan cheese, and egg together in a large bowl. Stir in 1 1/2 cup pesto. Add spinach and chicken mixture; stir to combine.

Spread remaining 1/2 cup pesto in the casserole dish. Arrange 4 lasagna noodles, slightly overlapping, in the bottom of the dish. Top with 1/3 of the ricotta spinach mixture and 1/3 of the mozzarella cheese. Repeat layers twice, ending with mozzarella cheese.

Bake in the preheated oven until bubbly and golden, 35 to 40 minutes.