Preheat oven to 325°F (160°C). Lightly grease a 9-inch springform pan, line bottom with parchment paper, and place on a baking sheet.
Pulse shortbread cookies in a food processor until fine crumbs form. Mix with melted butter until the mixture resembles wet sand.
Press the crumb mixture firmly into the prepared pan, slightly up the sides. Bake for 10 minutes, then cool completely on a wire rack.
Chop Twix bars into 1/2-inch pieces and set aside, reserving a few for garnish.
Beat softened cream cheese on medium speed until smooth and creamy. Add sugar and beat until fluffy. Add eggs one at a time, beating on low just until combined.
Add vanilla, sour cream, and caramel sauce, mixing on low until just combined. Fold in chopped Twix pieces gently with a rubber spatula.
Pour filling over cooled crust, smooth the top, and tap the pan gently to release air bubbles. Bake for 55-65 minutes until edges are set and center jiggles slightly.
Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour. Run a knife around the edges and cool to room temperature.
Refrigerate the cheesecake for at least 6 hours, preferably overnight, until fully firm.
Place chopped chocolate in a heat-proof bowl. Heat heavy cream until simmering, then pour over chocolate. Let stand 2 minutes, then stir until smooth and glossy.
Remove cheesecake from the springform pan. Pour ganache over the top and spread evenly with an offset spatula. Refrigerate 15-20 minutes to set.
Drizzle with caramel sauce, garnish with reserved Twix pieces, and serve chilled or at cool room temperature.