Combine the chocolate and 4 tablespoons of the butter in a medium microwave-safe bowl. Microwave on high in 30 second intervals, stirring in between each with a rubber spatula, until completely melted and smooth, 1 to 1 1/2 minutes total.
Brush a 12-ounce ramekin with the remaining 1/2 tablespoon softened butter and sprinkle lightly with granulated sugar. Place the ramekin on a baking sheet.
Add the egg, egg yolk, granulated sugar, espresso powder, vanilla extract and salt to the bowl of a stand mixer fitted with a whisk attachment. Whisk on medium-high until fluffy and pale, 1 1/2 to 2 minutes. Turn the mixer to low, add the flour and whisk for a couple of seconds to combine. Turn off the machine.
Add the chocolate mixture, turn on the machine and mix until just combined. Remove the bowl from the stand mixer and pour the batter into the prepared ramekin. Bake until the sides are firm but the center is still soft, 17 to 19 minutes. (A cake tester inserted into the center of each cake should not come out clean.) Do not overbake.
Let the cake cool for 1 minute. Invert onto a serving plate, sprinkle with confectioners' sugar and serve warm.