Preheat & Prepare: Preheat your oven to 325°F (163°C). In a medium bowl, mix the graham cracker crumbs, melted butter, and 3 tablespoons of sugar until evenly moistened.
Press the Crust: Press the crumb mixture firmly and evenly into the bottom of a 9-inch springform pan. Set aside.
Beat the Base: In a large mixing bowl, beat the softened Philadelphia cream cheese, 1 cup of sugar, and vanilla extract using an electric mixer on medium speed until the mixture is completely smooth and free of lumps.
Add Eggs Gently: Reduce the mixer speed to low. Add the eggs one at a time, mixing just until blended after each addition. (Do not overmix to avoid incorporating excess air).
Bake: Pour the smooth batter evenly over the prepared graham cracker crust. Bake for 55 minutes, or until the edges are set but the center still has a slight, gentle jiggle.
Cool & Chill: Turn off the oven. Loosen the cake from the rim of the pan with a knife, and let it cool completely at room temperature. Once cooled, refrigerate the cheesecake for at least 4 hours (preferably overnight) before slicing and serving.