Peel and slice the onion, garlic and ginger as thinly as you can. A mandolin is a great choice for this.
On the bottom of the canning jar, layer slices of onion, garlic and ginger about an inch thick.
Pour sugar over the onion mixture until you can't see it anymore from the top, making another layer about a half inch to an inch deep.
Add another inch-thick layer of onions, garlic and ginger slices, then pour in the sugar to cover. Repeat this process, making an onion and sugar "parfait" until the jar is almost full.
Top off with a bit more sugar and close the lid tightly.
In one hour, the sugar will be soft. In two hours, you will start to see liquid forming in the bottom of the jar. In three hours, you will see the syrup forming, and in four hours, the syrup will be complete.
Don't remove the onions, garlic and ginger from the syrup. Just press the mixture back with the spoon when you administer the syrup. Keeps for 6 months to a year unrefrigerated.
Take 2-3 times a day, as needed to soothe sore throat and wet or congested coughs.