Preheat the oven to 350°F (175°C). Lightly coat a 9 x 13-inch baking dish with the 1 tablespoon butter. (Optional: line the dish with parchment paper, leaving a 2–3 inch overhang on two opposite sides to lift the bars out later; butter the parchment as well.)
In a large bowl, whisk together 2 3/4 cups all-purpose flour, 2 cups sugar, 2 teaspoons baking powder, 1 1/2 teaspoons baking soda, and 1 teaspoon kosher salt until evenly combined.
Add 1 large egg, 3/4 cup melted butter, and 1/2 teaspoon vanilla extract to the dry ingredients. Beat or stir until the mixture is well combined and forms a sticky dough.
Press the dough evenly into the bottom of the prepared 9 x 13-inch baking dish to form the crust.
Evenly sprinkle 1 cup chopped pecans over the crust.
In a separate bowl, beat together 8 ounces softened cream cheese, 3 1/2 cups confectioners’ sugar, and the remaining 2 large eggs with an electric mixer or sturdy whisk until the filling is smooth and creamy.
Pour the cream cheese mixture over the crust and pecans, spreading it evenly with a spatula.
Bake in the preheated oven until the top is golden brown and the filling is set (center should not be liquid), about 45 minutes.
Remove from the oven and place the pan on a wire rack. If you used parchment, cool in the pan for about 5 minutes, then use the parchment overhang to lift the bars onto the wire rack to cool completely. If you did not use parchment, let the bars cool completely in the pan (you may run a knife around the edges after they have cooled slightly to loosen before cutting).
Once completely cool, cut into bars and serve.