Heat olive oil in a large frying pan over medium heat. Add garlic, and cook for a few minutes, stirring constantly. Add in the tomatoes and juice, vinegar and basil and simmer until the liquid has reduced by about half.
Place the broccoli on top of the tomatoes, and season with a little salt and pepper. Simmer over low heat for 10 minutes, or until the broccoli is tender. Do not over cook the broccoli, it should be a vibrant green. Pour into a serving dish, and toss to blend with the sauce before serving.