Preheat the oven to 350°F (175°C). In a 9-inch round cake pan, spread the melted butter evenly and sprinkle the brown sugar over it. Arrange pineapple slices on top of the sugar in a single layer.
In a bowl, combine graham cracker crumbs, 0.25 cup sugar, and 0.5 cup melted butter. Press the mixture firmly over the pineapple layer. Bake for 10 minutes, then remove from oven.
In a large mixing bowl, beat cream cheese and 1 cup sugar until smooth. Add eggs one at a time, then blend in vanilla extract.
Pour the cream cheese mixture over the crust and pineapple in the pan. Bake for 40-45 minutes or until the center is almost set.
Allow the cheesecake to cool in the pan on a wire rack, then refrigerate for at least 4 hours before serving.
Notes
For the best flavor, use fresh pineapple when available and refrigerate overnight for a firmer texture.