Combine first 4 ingredients; stir well. Firmly press crumb mixture onto bottom and 1 1/2" up sides of a lightly greased 9" springform pan. Bake at 325° for 12 to 15 minutes. Remove to a wire rack; let cool.
Beat cream cheese at medium speed of an electric mixer until creamy; gradually add 1 cup sugar and cornstarch, beating well. Add eggs, one at a time, beating after each addition. Stir in eggnog, rum, and brandy. Pour batter into prepared crust.
Bake at 325° for 1 hour. (Center will be soft.) Remove from oven and gently run a knife around edge of pan to release cheesecake from sides; return to oven. Turn oven off; leave cheesecake in oven, with oven door partially opened, 30 minutes. Let cool to room temperature in pan on a wire rack. Cover and chill 8 hours.
Remove sides of pan and top cheesecake with Sugared Rose Petals, if desired.