1. Cook pasta according to the package directions, omitting salt and fat. Drain pasta through a sieve over a bowl, reserving 1/4 cup pasta water. Rinse pasta with cold water; drain.
2. Combine basil, 3 tablespoons pistachios, oil, salt, and garlic in a food processor. Process until smooth, scraping sides. Transfer basil mixture to a large bowl; stir cheese and reserved 1/4 cup pasta water into basil mixture. Add pasta and tomatoes to basil mixture; toss gently to coat. Sprinkle with remaining 1 tablespoon pistachios. Serve with lemon wedges, if desired.
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