Preheat oven to 350.
Beat butter and sugar in large bowl.
Add eggs, one at a time, and vanilla extract, beating until smooth.
In a separate bowl, mix flour, baking powder, and salt.
Add flour mixture to wet ingredients and blend.
Stir diced apricots into dough.
Divide dough in half.
Shape each half into 11″ x 2″ rectangle, using floured hands.
Set each loaf 2″ apart on a parchment paper-lined baking sheet.
Bake for 30 minutes or until the dough is set.
Leaving the oven on, remove the biscotti loaves and cool for 15 minutes on cookie sheet.
Using a serrated knife, cut the loaves into diagonal slices, 1/2″ thick.
Place slices on cookie sheet with the cut sides down. Bake for 8 to 9 minutes.
Turn over slices, and bake for 8 to 9 minutes more.
Remove biscotti from oven, and allow to cool completely on a cooling rack.
Combine powdered sugar and milk, 1 teaspoon at a time, until a thick glaze is formed.
Coat each biscotti slice with glaze.
Allow glaze to set; then store in a sealed container.