Heat oven to 350°F. Prepare two muffin pans with cupcake liners.
Stir together sugar, flour, cocoa, baking powder, baking soda and salt in large bowl. Add eggs, milk, oil, vanilla extract beat on medium speed of mixer 2 minutes. In a measuring cup microwave 1 cup of water (or heat on stovetop). Stir in instant espresso. Add boiling water to batter. Stir to combine. (batter will be thin) to the cake batter. Fill each cupcake well about 3/4 cup full of batter.
Bake for 22-25 minutes or until wooden pick inserted in center comes out clean, rotating pans halfway through baking. Remove cupcakes from pans and allow to cool on a wire rack. Cool completely. Repeat with the additional cupcake batter (about 6 additional cupcakes)
To Make The Frosting: In a seperate bowl, chop your chocolate (unless you are using chips). Then in a saucepan or microwave safe bowl, heat the heavy cream and bailey's to a simmer. Pour over the chocolate and let sit undisturbed for 5 minutes. Whisk until smooth. Allow to cool and slightly harden, then whisk in a stand mixer until light and fluffy.
With a pastry bag and tip attached, pipe the frosting on each cupcake. Decorate with sprinkles. Store at room temperature for up to 2 days.Refrigate for up to 3 days, just bring back to room temperature before serving.