In a mixing bowl, beat softened butter with granulated sugar until creamy. Beat in eggs, espresso powder, and vanilla extract. Add flour and baking powder. Fold in caramel bits. The 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 from oven and let cool for about 10 minutes. Cut into 1-inch slices and arrange slices upright on the baking sheet. Bake for an additional 20 minutes. Remove from oven and cool completely before glazing.

For the glaze, whisk together powdered sugar, vanilla extract, espresso powder, and heavy whipping cream until smooth. Spread the glaze onto the cooled cookies. Allow to set for about 15 minutes.