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Step 1
Using ground crumbs: If your cookies are already crumbs, stir together crumbs, butter, 1/3 cup sugar, and salt. Press into the bottom and about 1 inch up the sides of a greased or buttered 24-centimeter springform pan (about 9.5 inches - yes, mine was this size, but otherwise I'd use a 9-inch pan). Bake for 8-10 minutes at 350F; set aside.
Step 2
Using whole cookies: Grind cookies in the food processor until finely ground; then add sugar, butter, and salt, and process until mixed. Press into the bottom and about 1 inch up the sides of a greased or buttered 24-centimeter springform pan (about 9.5 inches - yes, mine was this size, but otherwise I'd use a 9-inch pan). Bake for 8-10 minutes at 350F; set aside.
Step 3
Cook 1 cup sugar in a dry, heavy saucepan over medium heat, stirring, until melted and golden. This may happen suddenly. Cook without stirring until a deep golden, but don't let it burn. (This, too, may happen suddenly.) Remove from heat and carefully stir in heavy cream. The mixture will bubble and the caramel may harden. Return to heat and cook on low, stirring constantly, to dissolve the caramel. Remove from heat, add the chocolate, and stir until mixture is smooth. Stir in yogurt or sour cream.
Step 4
Beat cream cheese with an electric mixer until fluffy. Scrape down the sides and bottom, then add chocolate mixture on low speed. Add eggs one at a time, and then vanilla, scraping down the sides and bottom after each addition. Try not to whip in too much air.
Step 5
Pour filling into the crust. Place springform pan on another baking sheet (in case it leaks), then bake at 350F for 50-55 minutes. Cake will be set 3 inches from the edge, but the center should still be wobbly. Cake will set more as it cools.
Step 6
Remove cake from oven. If you're concerned it will stick to the sides, run a knife along the edge to loosen it. Chill cake, loosely covered, for at least 6 hours before serving. Cheesecake will last at 1 week.