Preheat oven to 350°F. Line an 8×8 inch baking pan with parchment paper with overhang on two sides and lightly grease.
Make the crumb mixture: In a large bowl whisk flour, granulated sugar, brown sugar, baking powder, salt, and lemon zest. Pour in melted butter and stir until moist crumbs form and no dry flour remains.
Press about 0.75 of the crumb mixture firmly into the prepared pan to form an even crust. Reserve the remaining crumbs for the topping.
Par-bake the crust for 10 minutes. Remove and set the pan on a rack; keep the oven at 350°F.
Make the filling: In a medium bowl whisk sweetened condensed milk, lemon juice, egg yolks, cornstarch, and vanilla until smooth. Let sit 2 minutes to begin thickening.
Pour the filling over the warm crust and spread into an even layer. Sprinkle the reserved crumbs evenly over the top.
Bake 20 to 22 minutes, or until the topping is lightly golden and the center is set but still slightly jiggly.
Cool completely in the pan on a rack, then chill for at least 60 minutes for clean slices. Lift out using the parchment and cut into 16 bars. Dust with powdered sugar before serving if desired.
Notes
For a sweeter bar, reduce lemon juice to 0.66 cup. For extra tartness, add 1 additional tablespoon lemon zest. Store covered in the refrigerator up to 5 days or freeze up to 2 months.