Rinse the basil leaves quickly in cold water, then dry them thoroughly in a salad spinner or by rolling them in a clean kitchen towel. Wet basil will not pound properly and will turn the pesto watery and dark.

Place the peeled garlic cloves and the coarse sea salt in a marble mortar. Using a wooden pestle, crush and grind them with a circular motion against the mortar walls until you have a smooth, creamy paste with no visible garlic chunks, about 1 minute.

Add the pine nuts and continue working them in with the same rotating pressure until they break down into a coarse, oily paste, about 1 to 2 minutes.

Add the basil leaves a small handful at a time. Do not pound downward; instead, press the pestle against the walls of the mortar and rotate, crushing the leaves gently to release their oils without bruising them. Rotate the mortar with your other hand as you work. Continue adding basil in stages until every leaf is worked into a bright green pulp. This takes 5 to 8 minutes and should never feel rushed.

Once the basil is fully broken down and the paste has turned a vivid, uniform green, add the grated Parmigiano Reggiano and Pecorino Fiore Sardo. Stir them in gently with the pestle until fully incorporated.

Drizzle the Ligurian extra-virgin olive oil in a thin, steady stream while stirring continuously with the pestle. Work the oil in until the sauce is glossy, creamy, and homogeneous but still shows tiny flecks of basil, nut, and cheese. Do not overwork it into a smooth puree.

Taste and adjust with a pinch more salt if needed. Use immediately at room temperature to dress hot pasta, tossing off the heat and thinning with a spoonful of pasta cooking water if the sauce feels tight. Never place the pesto over a flame.