Preheat oven to 350°F (175°C). Wrap the outside bottom of a 9-inch springform pan tightly with heavy-duty aluminum foil to prevent water bath leakage.

In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter until well mixed.

Press the mixture evenly into the bottom of the prepared springform pan.

Bake for 8-10 minutes, or until lightly golden. Remove from oven and let cool slightly while preparing the filling. Reduce oven temperature to 325°F (160°C).

In a small saucepan, mash the 2 ripe bananas thoroughly. Stir in 1 tablespoon of lemon juice.

Cook over medium-low heat for 5-7 minutes, stirring frequently, until the mixture thickens slightly and most of the moisture has evaporated. This intensifies the banana flavor and prevents excess moisture in the cheesecake. Let cool completely.

In a large bowl with an electric mixer, beat the softened cream cheese on medium speed until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl.

Gradually add 1 ½ cups granulated sugar and cornstarch, beating on low speed until just combined, then increase to medium and beat until smooth, about 2 minutes. Do not overmix.

Add the eggs and egg yolk one at a time, beating on low speed just until combined after each addition. Do not overbeat, as this can incorporate too much air, leading to cracks.

Stir in the sour cream, vanilla extract, and the cooled banana puree until just incorporated. The mixture should be smooth.

Pour the cheesecake filling over the cooled graham cracker crust in the springform pan. Gently tap the pan on the counter a few times to release any air bubbles.

Place the foil-wrapped springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan. This creates a water bath, which helps the cheesecake bake evenly and prevents cracks.

Carefully transfer the roasting pan with the cheesecake to the preheated oven (325°F/160°C).

Bake for 60-70 minutes, or until the edges are set, but the center still jiggles slightly when gently shaken.

Turn off the oven, crack the door open slightly, and leave the cheesecake in the oven for 1 hour to cool slowly. This also helps prevent cracks.

Remove the cheesecake from the oven and water bath. Carefully remove the foil.

Let cool completely on a wire rack at room temperature for at least 1-2 hours.

Once completely cool, cover loosely with plastic wrap and refrigerate for at least 6-8 hours, or preferably overnight, to allow it to set fully.

In a chilled large bowl with an electric mixer, beat the very cold heavy cream, powdered sugar, and vanilla extract on high speed until stiff peaks form.

Once the cheesecake is thoroughly chilled, carefully remove the sides of the springform pan.

Spread the whipped cream topping evenly over the top of the cheesecake.

If garnishing with fresh banana slices, toss them with a little lemon juice to prevent browning, then arrange them attractively on top of the whipped cream just before serving.

Slice with a warm, clean knife for best results.