Preheat the oven to 350 degrees F. Spray a 13x9-inch pan with nonstick spray.
PREPARE THE CRUST:
In a large bowl, use an electric mixer to beat the butter until fluffy. Beat in 2/3 cup powdered sugar. Add the 2 cups of flour a little at a time, beating until lumps begin to form. Press dough over the bottom of the prepared pan (use a fork or clean hands to press into an even layer). Bake until crust is light golden, about 20 minutes.
PREPARE THE FILLING:
While the crust is baking, beat the sugar and eggs in a medium bowl until blended. Beat in the lemon juice and zest, baking powder, and then flour. Pour the lemon filling over the hot crust. Bake until the filling is set in the center and browns on top (about 20 minutes). Transfer to a rack to cool.
When completely cooled, cut into bars. Dust with powdered sugar, if desired.
Notes
*These bars may be made one day ahead. Cover and refrigerate until ready to serve.