Start by bringing a medium pot of salted water to a boil.
Chop the Walnut (1/3 cup). Reserve a sprinkle for ganrish at the end.
Cut the Broccoli (1 head) so that you have florets only.
Once the water is boiling, place them in the water. Allow them to boil for about 3 minutes. Then, remove the florets with a slotted spoon and submerge in a large bowl of cold water. Allow to rest in the water until ready for use.
Keep that water boiling and add Salt (1 dash) and Pasta (16 ounce). Cook according to package. Strain pasta, but not completely. Leave about 1/2 cup of pasta water at the bottom. Place the pot of noodles aside for later use.
Juice the Lemon (1/2). You will need 1 tablespoon of juice.
In a food processor, combine walnuts, Garlic (2 clove), Basil Paste (1 tablespoon), 1 tablespoon lemon juice, Walnut Oil (1 tablespoon), Miso Paste (1 tablespoon), and Apple Cider Vinegar (1 teaspoon) and process until it's reached a fine consistency.
Strain the broccoli and add to the processor. Process until very smooth and creamy. Add the pesto sauce into the pot of noodles and stir well. You can add some extra salt here to taste.
Serve hot with additional walnuts.