I also peel a lot of ginger, so I started saving the ginger peels in a separate bag in the freezer, along with a few pieces of serrano chili. When I had about a cup of the stuff, I took it out and made this fantastic syrup: I boiled the ginger and chilies in water until the water took on the flavor, then I drained the liquid of the solid stuff, put it back in the pot, and dissolved some sugar in it. The result: intensely spicy and delicious syrup, not too sweet. I have used it in stir fries and curries, but mostly in cocktails. Even just mixed with soda water, it makes a fantastic ginger ale.
*Also, here is a soup I made with homemade stock: