1 Make the toffee sauce: Warm the heavy cream in the microwave for one minute, or on the stovetop over medium heat. The cream should steam, but not boil. Set this aside.
In a 4-quart saucepan, melt the butter over medium heat. Add the salt, brown sugar, and corn syrup. Whisking frequently, heat until the sugar has dissolved and the syrup bubbles gently. This should take anywhere from 3 to 5 minutes.
Turn the stove off and whisk in the warmed cream—be careful, as the sugar will bubble and steam once the cream is poured in. Add the vanilla extract to the sauce and set the pan back over medium heat.
Cook for another 5 minutes, or until the syrup is thick. Transfer the sauce to a glass jar and store in the refrigerator until ready to use, up to one week in advance.
2 Prep the oven and the pan: Preheat your oven to 350°F. Wrap a 10-inch springform pan in heavy duty aluminum foil and set aside; be very careful not to tear or puncture the foil.
3 Make the shortbread crust: Use a food processor to pulse the shortbread cookies into fine crumbs. Add 1/4 cup of granulated sugar and the melted butter to the food processor bowl and pulse until the crumbs hold together.
Squeeze a handful of crumbs in the palm of your hand. If the mixture doesn’t hold together, add another tablespoon of melted butter, and re-mix.
4 Pre-bake the crust: Press the shortbread mixture onto the bottom and an inch or so up the sides of the springform pan. Bake the crust for 10 minutes. Remove the pan from the oven and allow it to cool while you prepare the cheesecake filling.
5 Heat water: While the crust bakes, heat 4 or 5 cups of water to boiling for the water bath.
6 Prepare the banana cheesecake: In the bowl of a stand mixer with a paddle attachment (or in a large mixing bowl), blend together the cream cheese, the remaining 3/4 cup sugar, and the salt until smooth.
Add the eggs, one at a time, to the cream cheese mixture, stopping to scrape down the sides after each addition. Mix on low speed for an additional minute.
Add the banana puree and both extracts. Blend on low for another minute. Scrape down the mixing bowl and add the cornstarch. Blend on the lowest speed for 30 seconds, or until no lumps of cornstarch are visible, being careful not to over-mix.
7 Bake the cheesecake: Pour the batter into the prepared pan and set the foil-wrapped springform pan into a larger pan. Add enough hot water to reach halfway up the sides of the springform pan and carefully place the pan into the oven.
Bake the cheesecake for 55 minutes to an 1 hour, or until the top is a light golden brown and the cheesecake jiggles slightly when shaken. Turn the oven off and open the door a crack to allow the cheesecake to cool in the oven for 30 minutes.
8 Cool the cheesecake completely: Once the cheesecake has cooled in the oven, carefully take it out of the oven and remove the foil. Cool the cheesecake on the countertop for an hour, then transfer it to the refrigerator to cool completely, at least 12 hours or up to 24 hours.
9 Decorate the cheesecake: Once the cheesecake is cold, remove the collar from the springform pan. Warm the toffee sauce slightly so that it's pourable but not runny (I set it in a dish of warm water), then drizzle one cup of the toffee sauce over the top of the cheesecake. Use a piping bag to pipe rosettes of whipped cream around the cheesecake and garnish each rosette with a banana chip.
Keep the cheesecake refrigerated until ready to serve, and be sure to keep leftovers chilled, too.