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Step 1
Preheat oven to 325°. Place a greased 9-in. springform pan on a double thickness of heavy-duty foil (about 18 in. square). Wrap foil securely around pan. Place on a baking sheet.
Step 2
In a small bowl, mix cracker crumbs and sugar; stir in butter. Press onto bottom of prepared pan. Bake until lightly browned, 10-12 minutes. Cool on a wire rack.
Step 3
In a large bowl, beat cream cheese and sugar until smooth. Beat in sour cream, eggnog, cornstarch and vanilla. Add eggs; beat on low speed just until blended. Fold in peppermint candies. Pour over crust. Place springform pan in a larger baking pan; add 1 in. hot water to larger pan.
Step 4
Bake until center is just set and top appears dull, 60-65 minutes. Remove springform pan from water bath. Cool cheesecake on a wire rack 10 minutes. Loosen side from pan with a knife; remove foil. Cool 1 hour longer. Refrigerate overnight, covering when completely cooled.
Step 5
Remove rim from pan. Cut cheesecake into 12 slices; gently insert a wooden stick into the wide end of each. Place on a waxed paper-lined 15x10x1-in. baking pan; freeze until firm.
Step 6
In a microwave, melt chocolate and shortening; stir until smooth. Spoon chocolate mixture over each slice until all sides are coated; allow excess to drip off. (Keep remaining slices in freezer until ready to dip.) Place on a waxed paper-lined baking pan. Seal any gaps by drizzling with melted chocolate, reheating chocolate if necessary. Refrigerate 10 minutes or until set.
Step 7
Decorate with melted candy coating as desired. Refrigerate until serving.