Beat the butter and sugar together until light and fluffy. Beat in the eggs and vanilla.
In a small bowl, combine the flour, cocoa powder, baking soda, espresso powder, and salt.
Gradually add the dry ingredients to the wet ingredients until well combined.
Stir in the toffee chips.
Drop by heaping tablespoonfuls onto a parchment lined baking sheet.
Bake for 9 minutes or until just set. Cool for a few minutes on the cookie sheet and then transfer to a wire rack to cool completely before frosting.
To make the frosting:
In the bowl of a stand mixer, beat together the butter and powdered sugar until well combined. In a small cup, stir together the vanilla and espresso powder.
Add the espresso mixture to the butter mixture and beat until combined.
When the cookies are completely cool, spread half of the cookies with the frosting and top with the remaining halves.
Store any unused frosting in the refrigerator (or eat it with a spoon like me).