Preheat oven to 325°F and grease a 6" fluted tart pan with removable bottom.
In a small saucepan, melt the chocolate and butter on low-medium heat until the chocolate has completely melted. Stir well until the chocolate and the butter is combined. Remove from heat and set aside to cool.
In a mixing bowl, whip the sugar and eggs together with an electric mixer on medium speed until smooth and thick, about 4 minutes.
With the mixer on low speed, slowly pour the melted chocolate mixture into the egg mixture. Mix until combined.
Add in cocoa powder, espresso powder, salt, and vanilla. Use a spatula to fold to combine until no powdery bits remain.
This batter will continue to thicken as the melted butter and chocolate cools so pour it into the tart pan before it gets too thick to spread. Use a spatula to evenly spread the batter in the pan and smooth the top surface.
Bake for about 45 minutes or until a toothpick comes out almost clean. The middle of the cake will puff up in the oven and will deflate as it cools. Let cool for at least 20 minutes before removing the cake from the pan. Dust with powdered sugar and serve with a scoop of vanilla ice cream for best results!
Storing: This cake can keep at room temperature for 1-2 days but I prefer wrapping and storing in the fridge for up to 1 week. The cake texture becomes amazingly dense and fudgy after being in the fridge that I enjoy even more than freshly baked.