Preheat the oven to 375 degrees F (190 degrees C).
Place butternut squash, cut-side up, in a 9x13-inch baking dish; cover with aluminum foil.
Bake in the preheated oven until squash is tender, about 45 minutes. Cool slightly. Scoop flesh from butternut squash and transfer to a bowl; mash.
Cook and stir pine nuts in a dry, heavy skillet over medium heat until toasted and fragrant, 3 to 5 minutes.
Stir pine nuts, rice, bread crumbs, Parmesan cheese, basil, egg, ginger root, garlic, salt, and black pepper into mashed butternut squash until evenly combined; shape into patties.
Heat oil in a heavy skillet over medium heat; cook patties, working in batches, until crispy and browned, 3 to 5 minutes per side.