Toast the pine nuts. To toast in a skillet: heat a skillet over medium heat and add the nuts. Swirl the pan periodically until the pine nuts are golden and fragrant, approximately 5 minutes. To toast in the oven: Preheat to 350 degrees F. Spread the pine nuts in a single layer on a baking sheet, and toast until golden and fragrant, approximately 5 minutes. Gently shake the pan every 2 minutes, keeping an eye on them. Set aside to cool.
Prep the ramps: Wash the ramps thoroughly. Trim off and discard the root tips (just the tips, not the bulbs). Slice in half, separating the leafy green tops from the long stems and bulbs. Chop the stem side into approximately 1-inch pieces. Set the stems aside.
Blanch the ramps. Bring a large pot of water to a boil, setting a large bowl of ice water nearby. Once the water is boiling, add the green tops and blanch until bright green, approximately 15-30 seconds. Using tongs or a slotted spoon, transfer the greens to the ice water to halt the cooking process. Drain and then squeeze out most of the excess liquid.
Add ingredients to food processor. Add the ramps (both the greens and stems/bulbs), pine nuts, parsley, parmesan, and zest to a food processor. Pulse several times to chop, using a spatula to scrape down the sides of the bowl as needed. With the machine running, add 1/4 cup of the olive oil. If desired, add additional olive oil to thin out the mixture slightly. Add kosher salt to taste.
The pesto can be stored in the refrigerator for up to 5 days, or frozen for up to 3 months.
Pine nuts can be expensive, so other nuts may be substituted in their place. Slivered/blanched almonds or pistachios would be good options.