Parsley stems are perfectly edible but they can have a tough texture and slightly bitter taste, which is why a lot of home cooks just pick the parsley leaves off and use those. The stems of French or Italian parsley can be blended into homemade pesto or chopped on a cutting board to add crunch to your next salad. The flavor of the herbs is as rich in the stems as in the leaves, but if you don't like the woody texture or slightly bitter flavor, you might prefer to discard the stems and use the leaves only.