Cook pasta according to package directions in salted water. Once pasta is cooked, strain and cool under cold running water. Toss with a small amount of oil to prevent sticking. Make sure pasta is well drained. Place in a large bowl. Add the peas, asiago cheese and torn basil leaves.
In the bowl of a food processor or blender. Combine all dressing ingredients. Blend until well combined.
Pour dressing over pasta and toss until everything is well coated. Adjust salt and pepper to taste.