Grease bottom and sides of a 9-inch springform pan with 3-inch sides. Place the pan on a baking sheet to catch any leakage.
Prepare the brownie batter according to package instructions. Pour the batter into the prepared pan and bake for 30-35 minutes.
Remove from the oven and let it cool slightly.
Pumpkin Cheesecake layer
Using an electric mixer, beat the cream cheese and sugar together until creamy and smooth. Mix in the pumpkin puree, cornstarch, vanilla extract, salt, and pumpkin spice. Add eggs, one at a time, beating after each addition until just combined. Do not overbeat the batter.
Pour the mixture on top of slightly cooled brownie layer. Bake at 300 degrees Fahrenheit until the cheesecake is set but still slightly jiggly in the center, about 50-60 minutes.
Remove the pan from the oven and immediately run a thin knife around the edge of the pan, gently pressing into the side of the pan to avoid gouging the cake. This allows the cake to contract away from the sides of the pan as it cools, helping to prevent cracks.
Place the cheesecake on a cooling rack to cool completely in the pan. Cover and refrigerate overnight or for at least four hours.
Precut the cake into 8 or 16 pieces.
On a heat-safe work surface, sprinkle the tops of each piece with sugar and melt with a kitchen torch until it turns a deep amber color.
Refrigerate until ready to serve.
Make-Ahead Instructions - Make this cheesecake the day before. It has to chill for quite some time before serving.
Store Leftovers - Cheesecake will keep covered in an airtight container for up to a week. It can also be frozen up to 2 months. When ready to eat, thaw overnight in the refrigerator before serving.
Instead of prepared pumpkin pie spice, make your own: ½ teaspoon each: ground allspice and ground ginger plus ¼ teaspoon each: ground nutmeg and ground cloves.
You can also use an oven broiler to caramelize the sugar. Keep your eye on it as it can burn really quickly.
Instead of caramelizing sugar, serve the cheesecake slices with a dollop of whipped cream sprinkled with a pinch of nutmeg or cinnamon.
Please keep in mind that nutritional information is a rough estimate and can vary significantly based on products used.