Boil the broccoli florets in plenty of water for a few minutes until they are slightly tender. Take care not to boil more than that because then they will get mashed. Remove the broccoli and keep the water.

Boil the pasta in this water (adding more if necessary) according to the instructions on the packet.

Using a large frying pan sauté the garlic first, then add the broccoli and the cherry tomatoes and stir in the heavy cream. Take care when you stir so that you don't  mash the vegetables. Add the basil, season with salt and pepper and let it simmer for a while until the sauce thickens.

Mix with the vegetables and serve.