Bring a large pot of salted water to a boil. Cook pasta until just tender, about 10 minutes, or as package label directs.
While pasta is cooking, combine garlic, anchovies, lemon juice, mayonnaise, olive oil and 3/4 tsp. salt in a blender and blend until smooth.
Drain pasta. Toss with half of dressing and tomatoes. Let stand for 10 minutes. Toss with Parmesan.
Toss lettuce with remaining dressing and divide among 4 shallow bowls. Spoon pasta salad over lettuce, sprinkle with basil, if desired, and serve.
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