Center the rack and preheat the oven to 350°F (180°C).
Butter a rectangular mold of 8″ x 10″ (20 x 25 cm) and flour it.
Put the mold on a baking sheet.

The cake:
Sift together the flour, baking powder, baking soda, and salt.

In the mixer bowl, beat the butter at medium speed until it’s creamy. Add the sugar and beat for 3 minutes.
Add the eggs one by one, then the egg yolk, beating 1 minute after each addition.
Add the vanilla.
Reduce the mixer to low speed and add the dry ingredients in alternation with the buttermilk.
Pour the batter into the mold and smooth the top with a rubber spatula.

Bake for 28 to 30 minutes.
Transfer the cake to a cooling rack and let it cool to room temperature.

The extract:
Mix the espresso powder and boiling water in a small cup until homogeneous. Reserve.

The syrup:
Combine the water and sugar in a small saucepan and bring to a boil.
Add 1 teaspoon of coffee extract and the liqueur, mix and reserve.

The topping:
Put the mascarpone, sugar, vanilla, and liqueur in a large bowl and beat until smooth.

Whip the cream until it forms firm peaks and incorporate it into the mascarpone mixture with a spatula.

Assembly:
Cut the cake in half.
Moisten with the syrup, using a brush.
Spread 1/3 of the mascarpone mixture, then cover with the second half of the cake.

Frosting:
Add 1 1/2 teaspoons of coffee extract to the remaining mascarpone mixture and cover the cake with it.
Sprinkle with cocoa powder and refrigerate the cake for at least 3 hours before cutting into squares.