Prepare the ramps: Wash and thoroughly dry the leaves. Trim away the bottom roots of each bulb, much like you do with spring onions/scallions. Cut off and roughly chop each ramp bulb, then roughly cut or hand tear the leaves and stems.
Add the bulbs and walnuts to a food processor. Process until a thick paste develops, about a minute. Be sure to scrape down the sides of the bowl midway through.
Add the ramp leaves, cheese, salt, and pepper to the food processor bowl. Process until evenly combined.
With the processor still running, add olive in a slow steady stream until the pesto is the consistency your prefer. (See Note)
I prefer my pesto to be a thick paste, so, I don’t add much oil to the processor. When it’s time to dress the pasta, I’ll first coat the pasta with a little olive oil and then add the pesto. I find that a paste, also, works better when using pesto in other ways, like seasoning roasted chicken.