Preheat your oven to 350°F. Grease a mini muffin or cupcake pan generously.
In a medium bowl, mix together the graham cracker crumbs, 1/4 cup of sugar, and melted butter until the texture resembles wet sand.
Spoon around 1 1/2 tablespoons of this mixture into each cup of the prepared pan, pressing it firmly into the base and up the sides to create a small cup shape.
Bake for 6 minutes, then take it out and allow it to cool completely in the pan.
Meanwhile, finely dice the peeled and cored apples. Toss them in a bowl with 3/4 cup of water and lemon juice to prevent browning.
In a small saucepan, whisk together the cornstarch and the remaining 1/4 cup of water until smooth. Stir in the remaining sugar, cinnamon, and nutmeg.
Add the diced apples to the saucepan. Cook over low heat, stirring occasionally, until the apples are softened and the mixture has thickened slightly, about 8-10 minutes.
Once the graham cracker crusts have cooled, spoon about a teaspoon of the cooked apple mixture into each crust.
Place the pan back in the oven and bake for an additional 5 minutes.
Let the bites cool completely in the pan before removing and serving.