Combine 1 cup flour and 2 tablespoons sugar in a small mixing bowl; add melted butter, mixing well. Press mixture evenly into a 13- x 9- x 2-inch baking pan. Bake at 375° for 10 minutes.
Combine brown sugar, remaining 2 tablespoons flour, baking powder, chopped pecans, and eggs in a medium mixing bowl, beating until well blended. Pour over baked crust. Bake at 350° for 30 minutes. Let cool slightly.
Combine powdered sugar, lemon juice, and vanilla in a small mixing bowl; stir well. Spread over cake. Cut into 3- x 1 1/2-inch bars.