In a medium bowl stir together 1 cup of flour and 1/4 cup icing sugar. Cut in the butter until it looks like coarse meal; then work it with your fingers until the dough holds together. Press the mixture into the bottom of an ungreased 8" square pan and bake for 15 or until golden. Remove and leave the oven on.
In a medium bowl beat eggs until frothy. Gradually beat in the sugar. Add lemon zest and lemon juice; beat at high speed for 10 minutes, until smooth and slightly thickened.
In a small bowl combine the remain 2 Tbsp flour with baking powder and salt; gradually beating it into the lemon mixture, beat until smooth.
Pour over the baked crust and bake for 20 minutes, until set and lightly browned. Cool in the pan on a rack and then sift the remaining 1 tablespoons of icing sugar over the top and cut into 12 squares.