Bring a large pot of salted water to a boil and cook the trofie until al dente, about 10–12 minutes. Reserve about 1 cup of pasta water before draining.
Meanwhile, combine the basil, garlic, pine nuts, Parmigiano, salt, olive oil, and ice cubes to a food processor or blender.
Blend until smooth, creamy and bright green. Transfer the pesto to a large mixing bowl.
Add the hot trofie to the bowl with the pesto along with a ladle of the reserved pasta water. Toss continuously until the pesto emulsifies into a silky sauce that coats every piece of pasta. Add a little more pasta water if needed to loosen the sauce before serving immediately.
