Pull the feathery leaves off the stems. You should have about 2 loosely packed cups of leaves. Bring a small pot of water to a boil and drop in the carrot leaves. Cook for 1 or 2 minutes to blanch, and then drain. The greens will reduce to about ½ cup.
Transfer the greens to a food processor or blender and add the oil, pine nuts, garlic cloves, lemon juice, and salt to taste. Blend to a puree. Refrigerate the pesto for up to a week (it does ferment) or freeze.