Heat one tablespoon of olive oil in a skillet on medium heat. Add the 2/3 cups ramp bulbs and stems to the skillet and sauté until soft but not browned. Reduce heat if necessary.
Transfer to a food processor. Add the green tops, cheese, nuts and basil. Process until fi nely chopped, scrapping down the sides several times. With machine running, gradually add ½-cup olive oil and purée until smooth.
Season with salt and white pepper to taste. Transfer pesto to a bowl. Can be made a day ahead and refrigerated or frozen in ice cube trays. When frozen, transfer pesto cubes to a freezer bag.
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