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Heat your oven to 350°F (175°C). Line two baking sheets with parchment paper so the cookies release cleanly and the bottoms bake without catching.
In a large mixing bowl, beat the softened butter and granulated sugar for 2–3 minutes. The mixture should look a bit lighter in color and feel fluffy on the spoon. This gives you cookies with crisp edges rather than dense, flat discs.
Beat in the egg and vanilla extract until the mixture looks smooth and even. There should be no streaks of egg. At this point, the batter should feel creamy and slightly thick, not runny.
In a separate bowl, whisk together the flour, instant coffee, baking powder, baking soda, and salt. Break up any clumps of coffee so the flavor spreads evenly through the dough and you do not end up with bitter spots.
Add the dry ingredients to the butter mixture gradually, mixing on low speed or with a spatula until no dry flour remains. The dough should feel firm and hold its shape when you press it between your fingers. If it feels very soft or sticky, chill it for 15–20 minutes before shaping.
Scoop about 2 tablespoons of dough per cookie. Roll each portion into a ball between your palms to smooth any cracks, then place on the prepared baking sheets, leaving room between them. Gently flatten each ball with your fingers so you get even discs that will spread slightly in the oven.
Bake for 10–12 minutes, watching the edges. They should turn light golden while the centers look set and no longer shiny. The cookies will feel soft when hot but firm up as they cool. Let them rest on the tray for a couple of minutes, then transfer to a wire rack until fully cool.
In a clean bowl, beat the chilled mascarpone with powdered sugar and vanilla until smooth and creamy. This should take less than a minute. Stop as soon as it looks even so the mascarpone stays thick and does not turn watery.
In another bowl, whip the cold heavy cream until soft peaks form. When you lift the whisk, the peaks should stand up and gently fold over at the tip.
Gently fold the whipped cream into the mascarpone mixture in a few additions, using slow, sweeping motions. The frosting should look smooth and mousse-like, not runny. Chill until slightly firm, at least 1 hour, so it pipes neatly on the cookies.
Make sure the cookies are completely cool. Fill a piping bag with the chilled frosting or use a small spatula. Spread or pipe a swirl on top of each cookie, leaving a small border at the edge so the topping does not slide off.
Right before serving, lightly dust the tops with unsweetened cocoa powder using a small sieve. Aim for a thin, even layer so you taste both cocoa and mascarpone in each bite.