Bring a large pot of water to boil. Once it is boiling, add salt to the water. Then add the broccoli to the boiling water. Boil for about 5 minutes, until tender, but not too soft. Keep the water boiling because the cavatelli will be added to the pot.
While broccoli is boiling, heat olive oil in a pan, Once warmed through add full garlic cloves.
Add anchovy filets and let them melt into the oil.
Add chili flakes if using.
By this time the broccoli should be ready. Add half of the broccoli to the pan, and add the other half of the broccoli to a blender along with some warm water and salt, and blend it into a sauce. Turn the heat down on the pan with oil and broccoli, so that the broccoli doesn’t overcook.
Add the cavatelli to the boiling water and let them boil for 2-3 minutes (if using homemade cavatelli). If using store-bought cavatelli, they will most likely take longer to cook.
Once cavatelli are ready, add them to the pan with the broccoli, and add the pureed broccoli to the pan as well.
Turn the heat back up, and mix everything together. Remove the garlic cloves, and adjust for salt and pepper. Serve and enjoy!