Preheat oven to 325°F (163°C). Mix graham cracker crumbs, 0.33 cup sugar, and melted butter. Press into the bottom and slightly up the sides of a 9-inch springform pan. Bake for 10 minutes, then let cool.
In a large bowl, beat the softened cream cheese and 1 cup sugar until smooth and creamy. Add vanilla extract and sour cream, mixing until combined.
Add the eggs one at a time, beating on low speed just until combined. Do not overmix.
Pour the cream cheese filling over the cooled graham cracker crust. Smooth the top with a spatula.
Bake for 55-60 minutes, or until the edges are set but the center still slightly jiggles. Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour.
Remove from the oven and chill in the refrigerator for at least 6 hours or overnight.
To make the strawberry topping, combine strawberries, 0.25 cup sugar, and lemon juice in a saucepan over medium heat. Cook for 5 minutes until strawberries soften. Mix cornstarch with 1 tablespoon of water and stir into the saucepan. Cook for 1 more minute until thickened. Let cool.
Spoon the cooled strawberry topping over the chilled cheesecake before slicing and serving.
Notes
For best results, ensure all cold ingredients for the filling are at room temperature before mixing to avoid lumps.