Preheat oven to 325 degrees F . In a medium mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar and orange peel. Beat until combined, scraping sides of bowl occasionally. Add flour and beat until crumbly. Stir in the baking pieces with a wooden spoon, pressing dough together until smooth.

On an ungreased cookie sheet, press dough into a 12x8-inch rectangle (about 1/4 inch thick). Bake in preheated oven for 25 to 30 minutes or until bottom just begins to brown and center is set. Cool on sheet on a wire rack. Spread Orange Glaze over cooled shortbread. Let stand at least 30 minutes until glaze is set. Cut lengthwise into three strips. Cut each strip crosswise into eight pieces, making 24 rectangles. Cut each rectangle lengthwise into two pieces. Makes 48.

Orange Glaze: In a small mixing bowl, whisk together 1/2 cup sifted powdered sugar, 1 tablespoon softened butter, and 1 tablespoon orange juice. If necessary, whisk in additional juice, 1 teaspoon at a time, until glaze is of desired consistency.

Place cookies in layers separated by waxed paper in an airtight container; cover; store at room temperature for up to 3 days. Or freeze uncut shortbread for up to 3 months; thaw, glaze, and cut shortbread.