Bring a large covered pot of salted water to boil.
When the pasta water comes to a boil, cook the pasta in the salted water, stirring occasionally, until al dente, tender yet still firm to the bite.
Meanwhile, make the sauce:If using Mortar and Pestle: (about 10 minutes) (chunky)Pound and grind the garlic with the salt into a creamy paste. Add the pine nuts and pestle until smooth. Add most of the basil leaves, hand torn if too big, an ice cube, or the same amount of crushed ice, and gently pound and grind downward and with a wheel-like rotation, until it becomes a thick paste. (Save a few small leaves for later to sprinkle on or around the pasta.)Stir in the cheese with a wooden spoon.Slowly stir in the olive oil until incorporated. If using Food Processor or Blender: (smoother)Cool off the container and blade of the food processor, or blender, in the freezer for around 10 minutes before using.Blend garlic, salt, pine nuts until finely ground into a sandy texture. Add basil leaves, an ice cube, or the same amount of crushed ice, and use short pulses to roughly blend. Add the cheese and olive oil, and blend until combined. If needed, add as little extra olive oil as possible to help blend. (You can use hot pasta water to make it creamier later.) It should have an elegantly rustic, chunky texture. If using Immersion Blender: (smoothest)Place all ingredients (including olive oil) in a bowl and use short pulses until desired consistency.
Transfer the pesto sauce to a pasta serving bowl.
Drain the pasta (reserving 1/2 cup of the pasta water to use if needed), and toss with the pesto sauce. If the sauce seems a little dry, add 1 to 2 Tbsp of the reserved pasta water and stir until creamy.
Serve at once, sprinkled with grated cheese, small basil leaves, and a few whole pine nuts, with more cheese to be grated at the table for whoever wants it.
Pasta Substitutes:Short tubes: half penne, rigatoni (ideal to capture pesto); Twisted braids: casarecce, gemelli; Shells: conchiglie; Gnocchi: trofie (traditional), strozzapreti, potato gnocchi; Flat pasta: pappardelle (beautiful, yet a little more cumbersome to eat)
Cheese Substitutes:for Parmigiano: Grana Padano; for Pecorino Sardo: Pecorino Romano (saltier, so use less)
Variations:
Herb Variations: arugula, or parsley/marjoram blend
Green beans, snapped in thirds, or haricot verts, left whole or snapped. Add to boiling pasta water in the pasta's last 6 minutes of cooking.
Variations to Keep Basil Bright Longer: If you don't have ice, you can also use heat or lemon juice:
Microwave - Microwave the basil on high for 1 minute in a plastic bag. Blend into other pesto ingredients while hot, before adding the oil.
or Blanch - Plunge the basil into the boiling pasta water for about 5 seconds. Quickly fish out, sit on a paper towel to drain a little, and while still warm, blend it in with the other pesto ingredients, before drizzling in the olive oil. (Note, blanching can also diminish basil aroma, so keep it quick!)
Lemon - Add a squeeze of lemon with the basil. (Some people love the added tang of lemon, while others prefer not to change the fragrance and taste of the pesto.)
To Store: Fill a small container with pesto and, to prevent oxidation, pour a layer of olive oil on top and place plastic wrap directly on the surface (note: it usually gets a little darker on the surface anyway). Store in the refrigerator or freezer. Do not leave at room temperature.