Use very fresh, young basil. The smaller the leaves are, the better. If it's got flowers or buds on top, it will be bitter. Take the leaves off the stems and submerge in cold water for a few minutes while you get everything else together.
Peel a clove or two of garlic. Not too much. Remove the germ. I like to cut it up a bit into pea-sized chunks; makes it easier to grind. Throw it into your biggest mortar. Add a handful of very fresh pinenuts (check to make sure they aren't rancid!). Grind using a circular motion until it's a uniform, creamy consistency.
Lift the basil out of the water and lay them out on a towel. Pick out a few of the best-looking leaves for garnishes later. Roll the rest up in the towel, and twist the ends gently. They should be reasonably dry, but you don't want to wring the oils out of them. Put a handful of basil and a good pinch of coarse salt into the mortar. Keep grinding away until it's reduced to a paste. Add a couple more handfuls of basil and grind. Taste it. If it's still too garlicky, add another handful of basil and grind away.
Take out the pestle and scrape your pesto into a bowl. Add a few tablespoons each of grated parmigiano reggiano and pecorino sardo (if you can't find it you can use pecorino romano, which has a stronger flavor, but use less), and a healthy drizzle of the best olive oil you have. Stir it in with a spoon. Taste for salt.
Serve tossed with big squares of homemade pasta. I run my pasta through on the thinnest setting, then cut them into squares as wide as the sheets my pasta maker rolls out. It would be better to use a wooden rolling pin and roll out the pasta by hand, but I'm lazy. Anyway, toss the pasta with some pesto and a little pasta water, put it on warm plates, and spoon more pesto over the pasta. Garnish with a drizzle of olive oil, a dusting of cheese, and a couple basil leaves.