Flake the basil, wash in a colander and dry very well, chill to a bright green. Take a mortar and start by pounding the garlic, insert the pine nuts and continue to pound until a smooth paste is obtained, add the basil and coarse salt. Always proceed first with pounding motions and then continue with rotary motions.
Collect the ingredients from the inner edges of the mortar with a spoon so as to obtain a uniform pesto. When the consistency is creamy and homogeneous, add the pecorino cheese in chunks and pound in the same way to incorporate it, then also add the Parmigiano Reggiano and proceed in the same way, drizzle in the oil while pounding the basil with the various components until a homogeneous paste is obtained, adjust salt and pepper.
Genovese can be used immediately or stored in the refrigerator, inside a jar well covered with oil, for 4 days.
