Whisk together flour, cocoa powder, espresso powder, baking powder, and salt in a small bowl.
In a large bowl, add the butter and sugar and cream together, using an electric mixer, until light and fluffy. Beat in the eggs and vanilla, then slowly add the dry ingredients. Form the dough into a long 2-inch thick log on parchment paper and roll tightly. Freeze for at least 4 hours to overnight.
Arrange racks in the middle of the oven. Preheat the oven to 375 degrees F.
Slice the dough into 1/4-inch rounds and arrange them on a parchment lined baking sheet, about 1-inch apart. Bake for 12 to 15 minutes. Remove and let cool for 5 minutes on the baking sheet, then remove to a wire rack. Let cool completely before glazing.
Melt the chocolate and butter in a small glass bowl over a pot of simmering water. Whisk together until smooth and glossy. Remove from the heat and whisk in corn syrup and vanilla extract until smooth.
Dip the cooled cookies into the glaze and remove, with a fork, to a wire rack set over a sheet tray. Allow the cookies to set for 40 minutes before serving.