Preheat your oven to 350°F (175°C). Grease a 13×9-inch baking pan thoroughly or line it with parchment paper, leaving an overhang on the sides for easy removal later.
In a medium bowl, combine the flour, 1/2 cup of sugar, and salt. Cut in the 3/4 cup of softened butter using a pastry blender or your fingers until the mixture looks like coarse crumbs. Press this mixture firmly into the bottom of your prepared baking pan.
Place the crust in the oven and bake for 18 to 20 minutes, or until the edges are just starting to turn a very light golden brown. Remove the pan from the oven but keep the oven on.
While the crust is baking, whisk the eggs, corn syrup, the remaining 1/2 cup of sugar, melted butter, and vanilla extract in a large bowl until smooth. Stir in the chopped pecans until they are evenly coated.
Pour the pecan mixture over the hot, pre-baked crust. Spread it out evenly with a spatula. Return the pan to the oven and bake for an additional 25 to 30 minutes, or until the filling is set and no longer jiggles in the center.
Remove the pan from the oven and place it on a wire rack. Allow the bars to cool completely in the pan. Once cool, lift them out using the parchment paper and cut them into 24 squares.