Bring a stockpot of water to a boil. Drop in the broccoli and blanch until tender but still crunchy, about 2 minutes. Remove with a slotted spoon and place in a bowl. Rinse under cold running water until chilled. Drain thoroughly, then pat dry with paper towels. Place in a large serving bowl.

Cook the penne in the boiling water until al dente. Drain in a colander, then chill under cold water. Drain again, then pat with paper towels to absorb moisture. Place in the bowl with the broccoli.

Stir in the tomato, pine nuts, and basil. Mix the dressing with the Parmesan cheese and pour on the salad. Season with salt and pepper. Let sit at least 30 minutes before serving. If you are going to wait longer, cover and chill until 30 minutes before serving, then bring to room temperature.