Use an electric mixer to beat the butter in a large bowl- medium speed for 30 seconds. Add the sugar, baking powder, baking soda and salt; beat until combined. Beat in the 3 eggs, vanilla and almond extract until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour with a wooden spoon. Stir in the anise and fennel seeds, cranberries, pistachios and apricots. Cover and chill for 2 hours or until the dough is easy to handle.
Preheat the oven to 350°F. Divide the dough in half. Shape each half into a 12-inch long log about 1 1/2-inches thick. Place the logs 3 inches apart on a lightly greased cookie sheet. Flatten each log to a 3/4-inch-thick loaf. Whisk together the egg wash ingredients. Brush over the loaves.
Bake 25 to 30 minutes or until light brown. Cool loaves on cookie sheet for 1 hour or until completely cool.
When the loaves are cool, preheat the oven to 325°F. Transfer the loaves to a cutting board. Cut each loaf diagonally into 1/2-inch-thick slices. Lay the slices, cut sides down, on a cookie sheet. Bake in the preheated oven for 5 minutes. Turn the slices over; bake 5 minutes more or until the biscotti are dry and crisp. Transfer to a wire rack; cool.
Notes
HOW TO STORE THIS BISCOTTI: Place in layers separated by waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.