Core, peel, and slice each apple into roughly 12 pieces. If you’re working with smaller apples, cut them into fewer pieces. Don’t slice them too thin.
Melt the butter in a large saucepan over medium heat. When the butter is melted and gently simmering, add the apples. Note: If you coated the apples with lemon-lime soda, drain any liquid before adding them to the pan.
Lower the heat to medium-low, cover, and cook for about 5 minutes, stirring occasionally.
Add the sugar and cinnamon. Stir in the brown sugar, 4 tablespoons of water, and cinnamon. Mix gently to combine.
Still on medium-low heat, cover and cook for another 5 minutes, stirring occasionally.
Thicken the sauce. In a small bowl, mix 1 tablespoon of cornstarch with 2 tablespoons of water until smooth.
Add the cornstarch mixture to the apples and stir gently until incorporated. Cook, uncovered, over medium-low to low heat for 3–5 minutes, or until the liquid thickens. Stir occasionally.
Serve warm. They’re great as a sweet side for pork or chicken, or as a simple dessert with ice cream or whipped cream.