Set up a double boiler by placing a heatproof bowl on top of a saucepan filled with about 1 inch of water. Make sure that the bowl is not touching the water and is suspended above the water line by the rim of the pan.
Add the butter and the chocolate to the bowl and stir until melted and smooth.
Add the sweetener and espresso powder and stir until mostly dissolved.
Remove the bowl from the heat and let cool for a few minutes.
To the bowl, add the eggs, cocoa powder and vanilla extract, and using an electric mixer, beat on medium speed until smooth.
Pour the batter in the prepared springform pan and bake for 45 minutes, until cooked through, but still has a slightly fudgy center. Cool on a rack before serving.