Peel, core, and slice the Granny Smith apples into even pieces to ensure they cook uniformly. This also helps with texture later on.
Melt the unsalted butter in a large skillet over medium heat. Once melted, add the sliced apples from Step 1. Cover the skillet and cook over low heat for 15-20 minutes, stirring often to prevent sticking or burning, until the apples are softened.
While the apples are cooking, mix the white sugar, packed brown sugar, ground cinnamon, ground nutmeg, and a pinch of salt together in a bowl. This blend will add both sweetness and warmth to the apples.
Add the sugar and spice mixture from Step 3 to the softened apples in the skillet. Stir well to coat all the apples. Continue to cook over low heat for an additional 5-10 minutes, or until the sugar dissolves and the mixture becomes syrupy. I like to let it get a little bubbly so the sauce thickens.
Serve the warm, syrupy apples over scoops of vanilla ice cream for a classic treat. This also makes a great side for pancakes or oatmeal.