Wash and pat dry the nasturtium leaves. Check the flowers for bugs and dust and wipe impurities from the blossoms.
Place the leaves, cashews, garlic, nutritional yeast, salt, pepper, and lemon juice in a food processor and pulse until it breaks down and starts to blend together.
Add the olive oil gradually and pulse the food processor to incorporate.
Process the pesto until it reaches the consistency of pesto. This pesto will be a little more pasty than you might be used to.
Add the tablespoon of water to break it down a bit, and pulse until it is smooth.
At this point, if you want it a little more peppery, you can add some of the stems. Add the a handful at a time and see how you like the taste and texture.
Finally, add the nasturtium flowers, and just pulse gently until the blossoms are broken up and appear as colorful speckles in the pesto, without becoming completely pulverized into the pesto. Enjoy immediately or refrigerate for later.