Place the tomatoes in a small bowl; add boiling water. Cover and let stand for 5 minutes. Meanwhile, cook linguine according to package directions.
Place the basil, Parmesan cheese and garlic in a food processor; cover and pulse until chopped. Add the tomatoes with liquid, broth, walnuts, salt and pepper; cover and process until blended. While processing, gradually add oil in a steady stream.
Drain linguine; toss with pesto. Serve immediately.