In a nonstick skillet, add sausage and brown over medium high heat for about 4-5 minutes. Pour coca-cola and brown sugar into the skillet. Bring to a boil then reduce heat to medium low.
Stir and simmer anywhere from 10 to 40 minutes. (All stoves are different. On my stove, it takes about 30 minutes for these to caramelize. I've made these at friends' houses and it has taken 10 minutes. You have to eye ball it. You know your stove better than I do. What you're looking for is a thick, caramelized consistency so keep stirring until it becomes a thick glaze.)
Once the cola and brown sugar mixture become a glaze over the sliced sausages, remove the skillet from the heat. Transfer sausages to a plate and let cool for 10 minutes before serving. The sausages will be VERY HOT, please be careful. Enjoy!