Clean and wash the broccoli and cut it into small florets. Cook the pasta in boiling salted water according to the instructions on the packet. Cook the broccoli for the last 5 minutes. Wash and halve the tomatoes.
Mix pesto, vinegar, oil and 2 tablespoons of water. Drain the pasta and broccoli and leave to drain. Put the pasta, broccoli, tomatoes and olives in a bowl and stir in the dressing. Season to taste with salt and pepper.
Garnish with basil.