Use your steamer according to its instructions. Steam for about 4 minutes until the broccoli is just tender.
Fill a pot half way with water and bring to a boil on high. Tumble the broccoli pieces into the sieve and cover with a lid. Let it steam for 4 minutes until you can spear a piece with a fork and it meets no resistance.
Add the steamed broccoli, garlic, lemon juice, nuts, and cheese to the bowl of a food processor. Pulse until it is a crumbly paste that isn’t flying around. Slowly add the olive oil and continue to process. Add the water and process some more. Taste and add salt and pepper. Add more lemon juice or cheese or anything else you think it needs. It should be quite loose and smooth. If it is still quite chunky add a little more olive oil or water and continue to process it. It should be loose enough that it will easily coat the noodles when you toss them.
Now scrape about half the broccoli pesto into a bowl with your noodles and save the rest for another use (maybe another salad or on toast!). Or you can use it all if you’re so inclined of course!
Toss the noodles you made earlier with the pesto and you’re done!