Crush graham crackers to crumbs in a food processor or by placing in a resealable plastic bag and hitting with a meat tenderizer/mallet.
In a small bowl, combine the sugar with spices. Sprinkle sugar mixture and melted butter over crumbs and pulse to combine.
Divide the crust crumbs evenly into 12 cups of a mini cheesecake pan or into the cups of a mini muffin tin or standard muffin tin. For the mini cheesecake pan, you may have extra crumbs, which can be pressed into a separate small dish.
Press the crumbs down into each well to create an even layer.
Bake crust for 8 to 10 minutes. Remove from oven and set aside to cool.
Make the Filling:
Pat the pumpkin puree dry with paper towels if there is excess moisture. Set aside.
In a small bowl, whisk sugars, spices, and salt.
In the bowl of a stand mixer (or using a large bowl with a hand mixer), beat cream cheese for 1 minute.
Add half of the sugar mixture and beat for 1 minute, then add the rest of the sugar mixture and beat an additional minute.
Add the pumpkin puree, lemon juice, and vanilla and beat for 1 minute.
Beat the eggs into the pumpkin mixture 1 at a time. Add the heavy cream and beat for a final 1 minute.
Assemble and Bake:
Add the cheesecake filling batter to the wells of the pan. Fill to 3/4 full. You may have extra batter, which can be poured on top of the separate dish containing crust.
Bake for 15-25 minutes, depending on the size of the pan, until the filling is set. Remove pan from oven and cool to room temperature.
Place the pan in the refrigerator until ready to serve. Push mini cheesecakes up from the bottom and carefully remove the bottom pieces.
If desired, top mini cheesecakes with whipped cream and sprinkle with cinnamon, nutmeg, or pumpkin pie spice.