Take any leaves off the broccoli, and place the stalks in a large bowl.
Add the remaining ingredients and leave to marinate for 2 hours or more. You can also place the bowl, covered, in a dehydrator on 115 degrees F to speed up the wilting process. This also has the advantage of your broccoli being warm when you eat it.
For the pasta
Juice the beetroot and transfer to a large bowl. If you don’t have a juicer capable of doing this, then grate the beetroot instead of using juice.
Cut the tips off each end of the courgettes (zucchini), but leave the skin on.
Slice the courgettes with a mandoline. Then stack the slices up so you can cut them all together to make linguine-type strips.
Transfer the strips to the bowl with the beetroot juice and add the rest of the ingredients. Set aside whilst making the rest of the recipe. The longer you leave the courgette to marinade, the more purple it will be. For the photo example, I left it in overnight.
For the walnut pesto
Pulse all ingredients in a food processor, leaving the mixture slightly chunky.
Remove the courgette linguine strips from the beetroot juice mixture and place in a strainer to allow the excess liquid to run off. This may end in a lot of your kitchen being red! ?
In a different bowl, mix the walnut pesto with the purple pasta by hand, leaving some nice chunks.
Remove the broccoli, which should have softened but still be nice and crunchy, from the marinade and allow excess liquid to run off.
Arrange the broccoli on a plate however it works best for you.
Arrange the purple pasta and pesto on top of the broccoli.
The sauce in the picture was created by blending 1/2 cup of cashews with 1 cup of the remaining beetroot marinade in a high-speed blender.