It’s never a fun situation when you have a persistent cough. You don’t want to be that person in a quiet room during a lecture that can’t stop breaking the silence with your hacking, or that person at the restaurant that makes people fling themselves over their plates to protect their food while you cough away. Or that person on the plane that everyone throws disgusted looks at. Coughs are just terribly uncomfortable all around, both physically and otherwise.
The simplest way to make natural cough syrup is to boil your herb (or herbs) of choice in water. The resulting liquid is now an herbal tea which can be strained and taken on its own. If you want to make a syrup, however, you'll need to let the strained tea cool just a bit and then add honey to the mixture. The amount of honey you add will vary depending on the amount of tea you have, but the resulting mixture should be thick enough to coat the throat.
Chop the ginger and add it along with the peppermint to 4 cups of water. Bring to a boil and then lower the heat so that the liquid simmer. Simmer until the liquid has been reduced by half, than strain. Let it cool slightly, and then stir in 1 cup of honey until it has been dissolved completely. Bottle and take 1 tablespoon every few hours as needed to ease your cough. Keep refrigerated for up to 3 weeks.