Liquefy the butter gently in a microwave or a small saucepan over low-medium heat, transfer it to a large mixing bowl, and refrigerate for about 20 minutes until it reaches room temperature. Keep it below a bubbling simmer so it retains its moisture, and check that it no longer feels warm before continuing.

Stir both sugars into the cooled butter vigorously with a spatula for 1 minute, or use a stand mixer fitted with the paddle attachment. The mixture should look evenly blended, though the sugar will still give it a slightly grainy texture.

Work the egg and vanilla into the butter mixture until evenly incorporated. The wet ingredients should come together without separate streaks of egg.

Combine the flour, baking powder, baking soda, espresso powder, and salt in another bowl, then fold this mixture into the wet ingredients with a spatula. Stop when the flour streaks disappear to avoid overworking the dough.

Portion the dough into 11 cookies with a 2-tablespoon, 1.3-ounce scoop, roll each portion into a ball, and refrigerate on a parchment-lined tray for 1 hour. The chilled balls should feel firmer and hold their rounded shape rather than slumping.

During chilling, heat the oven to 180 °C / 355 °F, line a baking sheet with parchment, and bake 6 dough balls per tray for 10–11 minutes, one tray at a time. Look for set, matte edges surrounding soft centers that remain paler than the edges.

Leave the cookies on their baking sheet for 3 minutes, then slide a spatula underneath each one and transfer it to a rack to cool completely. The centers will firm during the tray rest, but the cookies should remain soft rather than crisp throughout.

Beat the cold mascarpone, cold heavy cream, confectioners sugar, vanilla, and agave or honey together in a medium bowl with an electric mixer, or use a stand mixer with its whisk attachment, stopping at stiff peaks and covering and refrigerating the cream if assembly will happen later. The finished cream should look smooth and silky, with peaks that stay upright when the whisk lifts.

At serving time, fill a piping bag fitted with a round tip such as Wilton 2A, spiral the cream from the center toward the edge of each completely cooled cookie, and sift the tablespoon of cocoa over the tops. The swirl should hold distinct ridges beneath a light, even cocoa coating.