Preheat oven to 350 degrees Fahrenheit. Line a 9"x13" pan (glass pan is preferred) with parchment paper so it hangs over the edges.
In the bowl of an electric mixer, add 2 c. flour, 3/4 c. powdered sugar, 1/8 tsp. salt and 1 Tbsp. cornstarch. Mix these dry ingredients quickly on low speed with the paddle attachment. Next, add softened butter and mix until large crumbs form (about quarter size). Press into prepared pan, ensuring it is an even thickness throughout.
Bake the crust for approximately 12-14 minutes, or just until set. Remember that it will continue to cook after adding the lemon mixture, so don't over-bake it (you don't want it to brown at all).
While the crust is baking, make the lemon layer by beating 4 eggs by hand with a fork in a large bowl. To the beaten eggs add 1 1/2 c. granulated sugar, 1 tsp. baking powder, 1/4 c. flour, 2 tsp. lemon zest, and 1/3 c. fresh lemon juice and stir together well with a spoon, making sure there are no lumps from the flour. Pour and spread evenly over baked crust. Return the pan to the oven and bake for approximately 18 minutes, or JUST until the lemon layer is firm and not jiggly. Don't let it brown on top (slight browning may occur around the edges). Bubbles on top is completely normal.
Let the bars cool for at least an hour at room temperature, before placing them in the fridge to chill completely through for about 1-2 hours. Best when served right out of the fridge, as the lemon layer will get runny in the heat. Dust the top with powdered sugar just before serving. Store in the refrigerator for up to 3 days.