Place diced tomatoes in a large mixing bowl and season with salt and pepper. Drizzle tomatoes with olive oil and set aside.
Bring a large pot of water to a boil, add salt. Cook pasta 1 minute less than required cooking time on package.
Combine basil, pistachio, garlic, Parmigiano-Reggiano cheese and romano cheese in a blender. Pulse on medium high for 15 seconds. Turn blender to medium speed and slowly drizzle in the remaining olive oil to emulsify the pesto. Add ice cubes and blend to combine. Pour pesto into a large mixing bowl.
Drain pasta and reserve 1/2 cup of the pasta cooking water. Add pasta and pasta cooking water to pesto.