Bring a large pot of water to a boil. Add fresh nettles and simmer for two minutes.
Drain nettles and pick them over to remove any large stems or twigs. Squeeze the nettles to remove the water.
Put the nettles in the bowl of a food processor. Add the walnuts, garlic, salt, lemon juice and zest, and pepper and pulse to incorporate.
With the motor running, stream in the olive oil and process until the pesto is silky smooth.
The pesto can be used immediately or frozen in small jars for later use. If you do freeze it, cover the top with a thin layer of olive oil to prevent freezer burn.