Pull the fronds of the carrot tops off the stems and discard the stems. Carrot tops have a firm, chewy texture, but the stems are tough. Wash and spin-dry the greens.
Pulse the garlic and walnuts briefly in a food processor, then add the various greens and the salt and pulse again, scraping down the sides of the container as needed, until the greens are finely chopped. Add the olive oil and lemon juice and process the pesto until it is smooth.