Preheat oven to 350°F (177°C). In a medium bowl, combine the graham cracker crumbs and 1/3 cup sugar. Pour in the melted butter and mix until the crumbs are evenly coated and resemble wet sand. Press the mixture firmly and evenly into the bottom and slightly up the sides of a 9-inch springform pan. Bake for 10 minutes, then remove and set aside to cool slightly. Reduce oven temperature to 325°F (163°C).

In the bowl of a stand mixer fitted with the paddle attachment, beat the softened cream cheese on medium speed until completely smooth and creamy, about 2 minutes. Add 1 cup of sugar and beat until combined. Scrape down the sides and bottom of the bowl. Beat in the sour cream and vanilla extract until just combined. On low speed, add the eggs one at a time, beating until just incorporated after each addition. Do not overmix after adding the eggs.

Pour the filling over the prepared crust. Smooth the top with a spatula. Wrap the bottom and sides of the springform pan tightly with aluminum foil to create a watertight seal. Place the pan inside a large roasting pan. Pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan. Bake for 55-70 minutes. The edges will be set, but the center will still have a slight jiggle when gently shaken.

Turn off the oven, crack the door open slightly, and let the cheesecake cool in the oven for 1 hour. This gradual cooling helps prevent cracks. Remove from the oven and water bath, then cool completely at room temperature on a wire rack. Once cool, cover loosely and refrigerate for at least 6 hours, preferably overnight.

In a medium saucepan, combine the sliced strawberries, 1/3 cup sugar, cornstarch, and lemon juice. Cook over medium heat, stirring frequently, until the strawberries release their juices and the mixture thickens to a glossy, syrupy consistency, about 8-10 minutes. Remove from heat and let cool completely to room temperature.

Once the cheesecake is fully chilled and set, run a thin knife around the inner edge of the springform pan to loosen it, then release the clamp. Spread the cooled strawberry topping evenly over the surface of the cheesecake. For clean slices, dip a sharp knife in hot water and wipe it dry between each cut. Serve on a white plate.