In a food processor, pulse together almonds, basil, garlic, and nutritional yeast until combined. Add olive oil and pulse until smooth. Season with salt and pepper.
Heat olive oil in a large skillet over medium heat. Add mushrooms and do not stir for several minutes until they are golden and crispy on one side. Stir and add squash, cook until squash is soft.
Meanwhile, cook the pasta according to the package instructions.
Turn heat to low and add kale and sun-dried tomatoes. Cook until kale is bright green, then add pasta and pesto. Stir until combined. Season with salt and pepper. Serve warm.