Toast ½ cup pine nuts in cast iron skillet or stainless steel skillet on the stovetop. Toss once halfway through, until golden brown, 5–7 minutes.
Transfer to mortar and pestle and let cool.
Add 3 oz. Parmesan and 2 garlic cloves, finely grated, and grind with pestle until finely ground, about 1 minute.
Add basil leaves a handful at a time and mash with other ingredients.
Add ¾ cup extra-virgin olive oil in a slow and steady stream while mixing until pesto is mostly smooth, with just a few flecks of green.
Season with 1 tsp. kosher salt. (Can also be made in a food processor if you have one.)
If using pesto with pasta, cook 12 oz. pasta in a pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving ½ cup pasta cooking liquid.
Place pesto and 2 Tbsp. unsalted butter, cut into pieces, in a large bowl. Add pasta and ¼ cup pasta cooking liquid. Using tongs, toss vigorously, adding more pasta cooking liquid if needed, until pasta is glossy and well coated with sauce. Season with salt.
Divide pasta among bowls. Top with grated Parmesan