Bring 4 quarts water and 1 T. salt to a boil. Add pasta and cook according to package directions for firm pasta (1 minute pasta al dente, usually 8 to 12 minutes depending on the exact noodle). Drain well and rinse with cold water.

Meanwhile, bring 2 quarts water and 1 tsp. salt to a boil. Fill a medium bowl with cold water and ice. Blanch the broccoli quickly until bright green and tender-crisp, about 3 minutes. Drain and immediately plunge into the ice water to stop the cooking. Drain well.

In a large bowl, whisk together mayonnaise, salad dressing, and Parmesan cheese. Stir in pasta, tomatoes, bell pepper, and scallions. Carefully fold in crab and stir until evenly coated. Chill until serving and refrigerate any leftovers.