How to Make It
Preheat oven to 350°F. Lightly coat the inside of a 9-inch springform pan with cooking spray; wrap the bottom of pan in a layer of aluminum foil, and place on a rimmed baking sheet.
Prepare the Crust: Process cookies in the bowl of a food processor until crumbs form. Add melted butter, sugar, and salt to food processor; pulse until combined. Firmly press crumb mixture evenly along bottom and slightly up sides of springform pan.
Prepare the Cookie Butter Cheesecake Layer: Beat cream cheese in a medium bowl with an electric mixer on medium speed until light and fluffy, about 5 minutes. Add sugar, and beat until combined and fluffy. Add cookie butter, vanilla, and salt; mix on medium speed until combined. Add eggs, 1 at a time, mixing until just combined. Pour cookie butter mixture into prepared Crust in pan; chill 15 minutes.
Prepare the Vanilla Cheesecake Layer: Beat cream cheese in a medium bowl with an electric mixer on medium speed until light and fluffy, about 5 minutes. Add sugar, and beat until combined and fluffy. Add sour cream, vanilla, and salt; mix on medium speed until combined. Add eggs, 1 at a time, mixing until just combined.
Spoon the vanilla cream cheese mixture over cookie butter mixture in pan; smooth top with a rubber spatula. Transfer springform pan on rimmed baking sheet to preheated oven; bake until center is nearly set, 45 to 55 minutes. Cool completely in the pan on a wire rack. Cover and chill 8 hours.
Prepare the Cookie Butter Caramel Sauce: Heat butter and brown sugar in a medium saucepan over medium-low, stirring often until butter and sugar melt. Whisk in cookie butter until melted and combined. Whisk in half-and-half, and cook, whisking constantly until smooth and heated through. Remove from heat, and stir in salt. Cool slightly.
Gently run a knife around the edge of cheesecake to loosen from pan. Remove the sides of springform pan. Pour caramel sauce evenly over top of cheesecake. Top with additional crumbled speculoos cookies if desired.