Mix garlic, soy sauce, vinegar, sugar, sesame oil, ginger, and pepper flakes in a 2-cup Pyrex measuring cup. Whisk in mayonnaise until smooth, then in a slow steady stream, whisk in oil to make an emulsified dressing; keep chilled until ready to toss with salad. Store in a clean jar with lid.
Bring 1 gallon of water and 2 tablespoons of salt to boil in a large soup kettle. Add pasta and, using package times as a guide, boil, stirring frequently and adding broccoli the last 1 minute, until just tender. Drain thoroughly (do not rinse) and dump onto a large, lipped cookie sheet. Set aside while preparing remaining salad ingredients.
Place all salad ingredients (except soy-ginger dressing) in a large bowl or transfer to a gallon-size zipper bag. (Can be covered and refrigerated several hours at this point). When ready to serve, add dressing; toss to coat and serve.