Separate the sliced onions into individual rings. Set them aside while preparing for cooking.
Heat the olive oil in a large skillet over medium heat. Add the separated onion rings from Step 1, kosher salt, and black pepper. Stir well to coat the onions evenly with oil and seasonings. Cook, stirring occasionally, for about 15 minutes, or until the onions are translucent and starting to soften.
Pour the Coca-Cola into the skillet with the softened onions and stir to combine. Continue cooking over medium heat, stirring occasionally, until the onions are golden, caramelized, and almost all of the liquid has evaporated. This should take about 15-20 minutes. I find that letting the onions get a little extra color adds wonderful flavor.
Remove the skillet from the heat. The caramelized onions are now ready to be used in your favorite recipes, such as burgers, sandwiches, or pizzas. Enjoy!