Preheat oven to 325°F (163°C). Lightly grease the bottom and sides of a 9-inch springform pan. Wrap the outside with heavy-duty aluminum foil to catch any drips.
In a medium bowl, combine 2 cups graham cracker crumbs and 3 tablespoons sugar. Stir in 6 tablespoons melted butter until the mixture resembles wet sand. Press firmly into the bottom and 1 inch up the sides of the pan.
Bake the crust for 10 minutes until lightly golden. Remove and let cool on a wire rack while preparing the filling.
In a large bowl, beat the softened cream cheese on medium speed for 2 minutes until smooth. Add sugar and cornstarch and beat until combined.
Add sour cream, vanilla extract, and lemon juice. Mix on low speed until just incorporated. Add eggs one at a time, beating on low after each addition until just combined. Fold gently with a spatula.
Pour filling over the cooled crust and spread evenly. Tap the pan on the counter to release air bubbles. Bake for 55 to 65 minutes until edges are set and the center has a gentle wobble.
Turn the oven off and leave the cheesecake inside with the door closed for 1 hour. Then crack the door open for 30 minutes. Remove and run a knife around the edge to release the sides.
Let cool completely at room temperature for 1-2 hours. Cover and refrigerate for at least 6 hours or overnight.
In a small saucepan, combine 1.5 cups raspberries, 3 tablespoons sugar, and 1 tablespoon lemon juice. Cook over medium heat until raspberries break down, about 5-7 minutes.
Stir in the cornstarch slurry and cook for 1-2 minutes until thickened. Strain through a fine mesh strainer to remove seeds, if desired. Cool to room temperature, then stir in remaining raspberries.
Remove the springform ring. Spoon the raspberry topping over the chilled cheesecake and spread gently. Garnish with fresh raspberries.