Cook pasta in a large saucepan of lightly salted boiling water until al dente, following packet instructions. Add the broccoli florets during the last 2 minutes of cooking; drain.
Preheat grill. Grill steak 10 cm from the heat for 4 minutes per side for medium, or until done to taste. Place on a cutting board; slice thinly across the grain, on the diagonal.
For the dressing, combine yoghurt, mayonnaise, vinegar, basil and salt in a food processor; process until smooth. Pour dressing into a large serving bowl.
Add the steak and any juices that have accumulated on the cutting board; toss to coat. Add pasta, broccoli, tomato and onion to bowl and toss again. (Recipe can be made ahead and refrigerated. Bring back to room temperature before serving.)