Heat oven to 350 degrees. Mix flour, baking powder, and salt in a bowl. Mix butter, sugar, vanilla, basil, and lemon peel in a separate bowl and beat with an electric mixer until well-combined. With mixer set on a low speed, slowly add the dry ingredients to the butter mixture. The mixture will be crumbly. Stir in the walnuts. Place dough in an ungreased 9x13" pan. Press dough into pan, ensuring an even thickness. Bake until the edges turn light brown, about 20 minutes. Do not overbake. Using a sharp knife, slice shortbread into 2" squares while hot. Let cool 10 minutes, then carefully transfer cookies to a plate or cooling rack.