Thoroughly rinse the kombu with water, making sure all the pickling salt has been washed off. Dab dry and cut into small pieces.
Puree the kombu, nuts, garlic, basil, arugula, olive oil, and lemon juice in a food processor until the mixture forms a smooth paste.
Put the pesto in a glass jar, cover with a layer of the olive oil, and store in the fridge for up to two weeks. Always serve with a clean spoon to maintain freshness.
Rinse the zucchini and grate them on the large hole setting of a box grater into spaghetti-like strings.
Mix the zucchini strings with the broccoli rabe, olive oil, and lemon juice. Spoon in the pesto, making sure the zucchini is thoroughly coated. Season with the pepper.