Peel and chop butternut squash. Lay on baking sheet in an even layer and drizzle with olive oil. Salt and pepper before placing in a 400 degree oven for 20 minutes.
Cook pasta according to package directions until al dente and drain. Reserve about 1/2 cup of pasta water.
Place kale leaves in a pot of boiling water. Cook for about 1 minute, then drain and place in a bowl of ice water to stop the cooking process. Drain excess liquid.
Place kale, garlic, pine nuts, and basil into a food processor or blender and pulse until finely chopped. Add the olive oil in a steady stream as you blend. Add the lemon juice, zest, sea salt and pepper and pulse again.
Transfer the cooked and drained linguine back into the pot over low heat. Toss with 1 cup of the kale pesto and mix. Add in starchy pasta water as needed to stir. When pasta is heated through, transfer to bowls.
Top with butternut squash, parmesan cheese and additional remaining pesto, if desired.