Heat oven to 300. Spray 9" sringform pan with cooking spray. Wrap foil around the pan to catch drips. In a small bowl, mix crust ingredients. Press mixture in the bottom of the pan. Bake for 8 to 10 minutes or until set. Cool 5 min to minimize cracking place shallow pan half full of hot water on the lower rack of the oven.
In large bowl beat cream cheese and sugar with an electric mixer on medium speed until light and fully. Beat in the eggs, one at a time, just until blended. Spoon 3 cups of mixture onto crust and spread evenly. To remaining mixture, add pumpkin, pumpkin spice and cardamom, mix with wire whisk until smooth. Spoon over mixture in pan.
Bake 1 hour and 15 minutes to 1 hour and 25 minutes or until the edge of cheesecake is set at least 2" from the edge of pan but the center of cheesecake jiggles slightly when moved. Run small metal spatula around cheesecake. Turn off oven and open door at least 4" and let cheesecake remain in the oven for 30 minutes. Cool in pan on cooling rack 30 minutes. Cover loosely, refrigerate at least 6 hours but no longer that 24 hours
In a small saucepan heat brown sugar, corn syrup and 2 tbsp butter to boiling over medium-low heat, stirring constantly. Boil 5 minutes, stirring occasionally. Stirring in whipping cream, heat and boil. Remove from heat, stir in Rum. Cool until warm.
Just before serving, run small metal spatula around edges of pan, carefully remove side of pan.