Preheat the oven to 350 degrees F.
Butter the sides and bottom of a 10-inch springform pan and set aside.
In the top of a double boiler, combine the butter, chocolate and coffee and melt slowly, stirring occasionally, until smooth. Remove from the heat and let cool for 5 minutes.
In a medium mixing bowl, whisk together the eggs, sugar and vanilla until frothy. Whisk the eggs into the melted chocolate until combined. Pour the mixture into the prepared pan. Bake for 1 hour and cool on a wire rack until it reaches room temperature.
Remove the sides of the pan, cover with plastic wrap and refrigerate overnight, before serving.