Preheat the oven to 350°F. Spray a 9-by-13-inch baking dish with cooking spray, then line the bottom and sides with parchment paper, leaving some overhang on all sides for easy removal.
In a large mixing bowl, use a handheld mixer to cream together the butter, brown sugar, granulated sugar, and vanilla until fluffy and well combined.
Add the flour, pecans, and salt. Mix on low speed until a soft dough forms.
Press the dough evenly into the bottom of the prepared pan. Chill the crust in the refrigerator for 15 minutes.
Transfer the pan to the oven and bake for 25 minutes, or until it turns light golden brown.
While the crust is baking, prepare the lemon filling. In a medium mixing bowl, whisk together the granulated sugar and flour until no lumps remain.
Add the eggs and mix until smooth.
Stir in the lemon juice and mix until fully combined. Set aside.
Once the crust is done, remove it from the oven and let it cool slightly, just until the bubbling stops, but the crust is still warm to the touch. (If the crust cools too much, the filling may seep underneath.)
Pour the lemon filling evenly over the warm crust.
Return the pan to the oven and bake for 20 minutes, or until the center is just set and no longer jiggly.
Remove from the oven and cool at room temperature for 30 minutes. Then refrigerate the bars for at least 2 hours, or until fully chilled and set.
Once chilled, lift the bars out of the pan using the parchment overhang.
Dust with confectioners' sugar, slice into squares, and serve.