Preheat the oven to 325°F. Lightly grease a 9-inch springform pan and line the bottom with parchment paper.
In a medium bowl, combine the graham cracker crumbs, 1/4 cup granulated sugar, 1/4 teaspoon kosher salt, and melted butter. Mix until the crumbs are evenly moistened.
Press the crumb mixture firmly into the bottom of the prepared springform pan, using the bottom of a measuring cup to create an even layer.
Bake the crust for 8 to 10 minutes, until lightly fragrant and just starting to turn golden at the edges. Remove from the oven and let cool while you prepare the filling. Reduce the oven temperature to 300°F.
In a large mixing bowl, beat the softened cream cheese with 1 cup granulated sugar and the remaining 1/4 teaspoon kosher salt on medium speed until completely smooth and fluffy, 2 to 3 minutes, scraping down the bowl as needed.
Add the sour cream and heavy cream and mix on low speed until fully combined and smooth.
Add the eggs one at a time, mixing on low speed just until each egg is incorporated before adding the next. Do not overbeat.
Mix in the vanilla bean paste until just combined, then gently fold in 1 cup of the chopped toffee bits.
Pour half of the cheesecake batter over the cooled crust and smooth into an even layer. Drizzle 1/4 cup of caramel sauce over the surface and gently swirl with a knife or skewer.
Pour the remaining batter over the swirled layer and smooth the top. Tap the pan gently on the counter a few times to release any air bubbles.
Place the springform pan on a rimmed baking sheet. Set the baking sheet on the middle rack of the oven. Place a separate pan of hot water on the rack below to create steam.
Bake at 300°F for 55 to 65 minutes, until the edges are set and the center jiggles slightly when you gently move the pan.
Turn off the oven, crack the oven door slightly, and let the cheesecake sit in the oven for 45 to 60 minutes to cool gradually.
Remove the cheesecake from the oven and run a thin knife around the edge of the pan to loosen the sides. Let cool completely to room temperature on a wire rack.
Once cooled, cover the pan tightly with plastic wrap and refrigerate for at least 4 hours, preferably overnight, until fully chilled and firm.
Just before serving, remove the sides of the springform pan. Drizzle the top of the cheesecake with the remaining 1/2 cup caramel sauce and spread or swirl gently.
Sprinkle the remaining 1/4 cup chopped toffee bits evenly over the caramel, pressing lightly so they adhere. Slice with a sharp knife wiped clean between cuts and serve chilled.