Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
In a bowl, combine the graham cracker crumbs, melted butter, and 1/4 cup granulated sugar for the crust. Mix until evenly coated. Press the mixture firmly into the bottom of the prepared pan and slightly up the sides to create an extra-thick crust. Use the back of a spoon or a flat-bottomed glass to press it down firmly.
Bake the crust in the preheated oven for 10-12 minutes until lightly golden. Remove from the oven and let it cool while you prepare the cheesecake filling.
In a large mixing bowl, beat the softened cream cheese until smooth. Add the 1 cup granulated sugar and 1 teaspoon vanilla extract; beat until fluffy and well combined.
Add the eggs one at a time to the cream cheese mixture, scrape down the sides of the bowl as needed.
In a separate bowl, mix together the room-temperature sour cream and heavy cream. Sift 1/4 cup all-purpose flour into the sour cream and heavy cream mixture. Stir until just combined.
Gently fold the sour cream, heavy cream, and flour mixture into the cream cheese mixture using a spatula.
Pour the cheesecake filling over the cooled crust. Smooth the top with a spatula.
Bake the cheesecake in the preheated oven for 55-60 minutes or until the edges are set but the center is slightly jiggly.
Turn off the oven, crack open the door, and let the cheesecake cool in the oven for 1 hour to prevent cracking.
After cooling in the oven, remove the cheesecake and let it cool completely at room temperature. Then refrigerate for at least 4 hours or overnight to set completely.
For the strawberry sauce topping, combine the sliced fresh strawberries, 1/4 cup granulated sugar, cornstarch, water, and lemon juice in a saucepan.
Cook the strawberry mixture over medium heat, stirring constantly, until it thickens and the strawberries soften (about 5-7 minutes). Remove from heat and let it cool slightly. If you want a thicker sauce, cook it for an additional 5-7 minutes, stirring constantly.
Pour the slightly cooled strawberry sauce over the chilled cheesecake. Spread it evenly with a spatula.
For the whipped cream topping, beat the heavy whipping cream, powdered sugar, and vanilla extract together until stiff peaks form.
Pipe or spoon the whipped cream onto the chilled cheesecake before serving.
Slice and serve the cheesecake with extra strawberry sauce on the side.