Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan lightly with butter.

In a medium bowl, mix the graham cracker crumbs, melted butter, and 1 tablespoon of sugar. Press the mixture firmly into the bottom of the prepared pan. Bake for 10 minutes, then let it cool.

In a large mixing bowl, beat the softened cream cheese and 1 cup of sugar until smooth and creamy. Use medium speed to avoid adding too much air.

Add the pumpkin puree, vanilla extract, and pumpkin pie spice. Mix until everything is well combined and the color is consistent.

Add the eggs one at a time, beating on low speed just until each egg is incorporated. Do not overmix.

Pour the pumpkin filling over the cooled crust and smooth the top with a spatula.

Bake for 55 to 65 minutes. The edges should be set, but the center should still have a slight jiggle.

Turn off the oven and crack the door open. Let the cheesecake cool inside for 1 hour to prevent cracking.

Remove the cheesecake from the oven and let it cool completely at room temperature. Refrigerate for at least 6 hours, or preferably overnight.

Combine the brown sugar, heavy cream, and butter in a small saucepan over medium heat. Whisk until the sugar dissolves and the sauce thickens slightly (about 5 minutes). Let it cool.

Once ready to serve, drizzle the caramel sauce over the chilled cheesecake and top with chopped pecans if desired.