1. Crush the basil, garlic cloves with salt in a mortar and pestle or in a food processor enough to form a coarse paste. Add the pine nuts and process or crush until there is a bright green paste. Add the grated Grana Padano and pecorino cheeses and pulse in food processor or stir in with a pestle and mortar. The pesto should be thick. Add in the olive oil to loosen.
2. Scrape the pesto into a small bowl or container and pour a thin film of olive oil over the top surface to prevent it from discoloring. It can stay at room temperature for a couple of hours before being used.
1. Bring salted water to a boil in the large pot (at least 6 quarts with 1 tablespoon kosher salt). Drop in the potato chunks, stir, and cook them for 10 minutes, then add the green beans. Cook the beans and potatoes for another 10 minutes and then add the trofie pasta to the pot and cook 5 minutes until the trofie is al dente.
2. Set the large skillet over very low heat, just to warm it, or warm the serving bowl, whichever you’ll use for the dressing the pasta. Scrape the pesto into the pan or bowl and loosen it with a bit of the pasta boiling water (don’t cook the pesto, just warm it).
3. When the vegetables are tender and the pasta is al dente, lift everything for the pot with a spider and tongs, drain briefly, and drop into the skillet or bowl. (If you prefer, drain the pasta and vegetables into a colander, being sure to reserve a cup or so of pasta cooking water before you pour it out.) Toss pasta, vegetables, and pesto together well – moisten with more pasta water if needed – then sprinkle the grated cheeses over, and toss again. Serve immediately in warm bowls with extra gratings of Grana Padano.