In a mixing bowl, beat butter with sugar until creamy. Beat in eggs, espresso powder and vanilla. Add flour and baking powder. Fold in caramel bits. Batter will be sticky.
Divide dough in half and form two 10x3 inch logs on a parchment paper lined baking sheet. Bake in a 350 degree oven for 25 minutes. Remove and cool about 10 minutes. Cut into 1 inch slices and arrange slices upright in pan. Bake an additional 20 minutes. Remove and cool completely before glazing.
For the glaze, whisk all the ingredients together until smooth. Spread onto cooled biscotti. Allow to set, about 15 minutes. Store in airtight container up to two weeks.