In a food processor, combine the basil, garlic, cream, half and half, stock, pine nuts, and half the parmesan until very smooth. The mixture will be thin; add more half and half if needed to thin it out to make 2-3 cups of sauce. Taste the sauce and add salt and pepper to your preference; set aside. The mixture should taste sightly salty as it will be flavoring the noodles and squash in the lasagna.
Layer the lasagna in the following order: make a thin layer of the pesto sauce in the bottom of a large baking dish. Top with an even layer of noodles, then an even layer of squash planks, layered like the noodles. Sprinkle with a handful of the cheese, then pour over a bit more sauce - ½ cup or so. Repeat 3 or 4 times until all the ingredients are used, ending with noodles, cheese, sauce, and the rest of the parmesan. Sprinkle the top of the lasagna with a few extra pine nuts.
Bake as the noodle box instructs, then let the lasagna rest for 15 minutes. Slice gently into squares and serve!