Boil a pot of salted water for your pasta. Prepare the pasta according to package directions.
In the meantime, place all sauce ingredients in a blender. Blend until relatively smooth. I usually blend for about 5 minutes, giving the blender a break every minute or so so that the motor doesn’t overheat. If you have a high speed blender it will be faster.
Make the broccoli:
Preheat a large heavy bottomed pan over medium heat. Saute the broccoli in one tablespoon of olive oil and a pinch of salt for about 5 to 7 minutes, tossing often, until it is a bright green. Add a few splashes of water if it seems dry.
Now push the broccoli to one side of the pan, and add the garlic. Immediately drizzle the one teaspoon of olive oil over the garlic and toss to coat, then integrate the garlic with the broccoli and cook for another minute.
Assemble:
Drain the pasta and add it immediately back to the pot you boiled it in. Add the sauce and parsley and toss to coat. Taste for salt and seasoning. Serve with broccoli!