Preheat oven to 350°F (180°C)
In a medium bowl, mix graham cracker crumbs, 1/4 cup sugar, and melted butter
Press the crust mixture into a 9-inch springform pan using the bottom of a measuring cup for even thickness
In a large bowl, use an electric mixer to cream cream cheese and 1 1/4 cups sugar on medium speed until smooth
Add eggs one at a time, mixing thoroughly after each addition
Beat in vanilla extract until fully incorporated
Pour filling over prepared crust and smooth the top with a spatula
Place springform pan on a baking sheet and bake for 50–60 minutes, until the center is almost set and the edges are firm
Let cool completely at room temperature, then refrigerate for at least 4 hours or overnight
Gently run a knife around the pan and release the springform before serving