First heat some pasta bowls ready for serving.
Then in a large saucepan heat 2.25 litres of salted water and bring it up to a good fierce boil. Add the pasta, stir once and let it boil briskly for 10 minutes without a lid.
Meanwhile make the pesto, place the basil, garlic, pine nuts and olive oil together with some salt in a mini-chopper and whizz, then push any unblended basil leaves down with a spatula and whizz again until you have a smooth purée.
Then transfer the purée to a bowl and stir in the grated Pecorino Romano cheese.
Next trim the beans and cut each one into three. Wash and slice the potatoes next leaving the skins on, they need to be about 3-4mm thick.
After the pasta has been cooking for 10 minutes, throw in the beans and potatoes. Now give the ingredients another stir and bring the water back to boil, then set the timer for 8 minutes.
After that drain the pasta, potatoes and beans in a colander, not completely as they need a little water still clinging to them. Then tip everything back into the saucepan, add the pesto sauce, and stir it pretty niftily to give everything a good coating.
Serve in the hot pasta bowls with the extra Pecorino Romano in a bowl to sprinkle over.
A good accompaniment would be some salad leaves sprinkled with a little extra virgin olive oil and some freshly squeezed lemon juice.
If you want to make pesto a few days ahead - cover the surface with some cling film, making sure the cling film actually touches the surface of the sauce. You can keep it in the fridge for a week.