In a 1-quart pitcher or mixing bowl with a spout, whisk together cocoa powder, espresso powder and a splash of heavy cream. Whisk in more cream a little at a time, until it reaches the consistency of a paste.
Whisk in the sweetened condensed milk, vanilla and Irish whiskey. Stir in the remaining heavy cream.
Pour or decant with a funnel into a 1-quart carafe or bottle. Store in the refrigerator, covered, for up to 2 weeks.