1. For the pesto, pick the basil leaves (don't wash them, just wipe them), then pound the garlic with the coarse salt and pine nuts in a mortar or blender to a paste; add the basil in batches and work until creamy.
2. Stir in the grated parmesan and pecorino, then drizzle in enough extra virgin olive oil to make a thick, glossy pesto.
3. Peel the potatoes and cut them into 1 cm cubes; trim the green beans and cut them into 3 cm pieces.
4. Boil the potatoes and beans in a large pot of salted water for 5 minutes, then add the pasta and cook everything together for the time given on the pasta packet.
5. Set aside a ladleful of cooking water, drain the pasta with the vegetables and toss thoroughly in a large bowl with the pesto and 2-3 tablespoons of cooking water.
6. Serve at once with a little grated parmesan - pesto is never heated, only warmed by the hot pasta.
Tip: The potato starch makes the pesto creamier - in Liguria this is the classic "complete" version; pesto keeps for 3 days in the fridge covered with oil.
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