Preheat the oven to 350 degrees and line an 8x8 baking pan with parchment paper. Stir the graham cracker crumbs with the melted butter until evenly moistened, then press the mixture firmly into the bottom of the pan.
Beat the cream cheese with the granulated sugar until smooth. Add the first egg and vanilla extract, then mix until fully combined. Spread this filling evenly over the crust.
In a separate bowl, stir together the pecan halves, corn syrup, brown sugar, and the remaining 2 tablespoons of butter. Beat in the second egg until the mixture is uniform.
Pour the pecan mixture over the cream cheese layer and spread it gently to cover the surface. Bake for 35 minutes, or until the top is set and lightly golden.
Cool the pan completely on a wire rack, then refrigerate for at least two hours before cutting into four squares.