Mix all ingredients together with a wooden spoon. Gently knead the mix together to form a dough ball. Turn the dough out onto a floured work surface and cut into three equal portions. Working with one portion at a time roll the dough into a long rope about 3/4 inch long dumplings. Cut into ½ inch long dumplings. Using your thumb, roll each dumpling gently across gnocchi board. Gather onto a baking tray dusted with semolina flour. Cook in salted boiling water for about two minutes until they all float to the surface. Drain and toss with sauce of your choice.
Place the basil leaves and a generous pinch of sea salt in the bowl of a mortar and pestle. Smash vigorously to a paste. Add the garlic and continue to grind the mix. Add the pine nuts and pulverize into the mix. Slowly drizzle the olive oil into the paste while continuing to mix and grind into a steady motion. Add the pecorino and stir to incorporate. Finish with a small squeeze of lemon juice and adjust seasoning with a bit more sea salt if necessary.