In a food processor, pulse the parmesan cubes until it has turned into a course grind.
Add in nuts, oil, basil and salt. Blend for 25- 30 seconds until it has a nice saucy consistency but is not smooth. The sauce should still have some texture to it.
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Bring a pot of water to a boil and add in a strong pinch of salt. cook the spaghetti for 9 minutes or longer if you prefer a softer bite. Reserve a cup of pasta water and strain the noodles.
Return the pasta to the pot you cooked it in along with the pesto and a splash of pasta water. Gently stir the pasta and pesto together until they have formed a slightly creamy pasta. adjust seasoning and consistency as needed with salt, parmesan and pasta water.
Serve each portion with additional parmesan and pine nuts