Fill a large pot with 7 litres of water. Bring the water to a boil over high heat. Reduce the heat to low and add 70 grams of sea salt. Do not add oil to the water.
When the water is boiling again, add the trofie and potatoes to the water, stirring occasionally.
Five minutes before the end of the cooking time indicated on the package of the pasta, add the green beans.
When the pasta is done, drain the water (reserving ½ cup of pasta water). Do not rinse the pasta. Divide the mixture evenly between 4 pasta bowls. Spoon the pesto into the bowls, stirring with the wooden spoon until evenly coated. Add 20 to 30 ml of pasta water a spoonful at a time to each bowl to loosen the sauce.