Bring a large pot of salted water to a boil. Peel and cut the potatoes into small cubes about ½ inch (1cm) thick and cut the green beans into bite-sized pieces (cut into 2 or 3).
To make the pesto add the basil, pecorino, peeled garlic clove, pine nuts and olive oil to a small bowl and use an immersion blender to blitz to a smooth paste. Alternatively, you can use a mortar and pestle. Season with a pinch of salt and set aside.
Add the pasta and the potatoes to the boiling water, after 5-6 minutes add the green beans and cook together until the pasta is al dente and potatoes cooked through (about 9-10 minutes altogether).
Reserve ½ cup (120ml) of pasta water then drain the pasta and veggies.
Add 1-2 tablespoons of pasta water to the pesto so it goes from a paste like consistency to a thick sauce consistency.
Add the pesto to a large mixing bowl then add the pasta, potatoes and green beans with a good pinch of salt. Mix until combined with the pesto. Add more water, if needed.
Check for seasoning and add more salt if needed, serve.