Make the cream. In a large bowl, combine the mascarpone, heavy cream, powdered sugar, espresso, and vanilla. Beat with an electric mixer on medium speed until soft peaks form and the mixture is thick and pipeable, 2–3 minutes. Don't overbeat, or the mascarpone can turn grainy.
Fill a piping bag. Transfer the cream to a piping bag fitted with a round tip (or snip the corner of a zip-top bag).
Pipe the topping. Pipe a ring of small cream dollops around the top of each donut, following the donut's circular shape. Leave the center hole open.
Dust with cocoa. Using a fine-mesh sieve, dust each donut generously with cocoa powder just before serving.
Serve immediately with hot espresso on the side.