Preheat oven to 375°F. Line a baking sheet with parchment paper, making sure to leave a bit of extra paper hanging over either end.
In a small bowl, whisk the flour, espresso powder, baking powder, baking soda, and salt together. In a larger bowl, mix the sugar with the Greek yogurt and half and half until combined. Fold the dry ingredients into the wet ingredients.
Pour the batter onto the lined baking sheet, using a rubber spatula to spread out to a thin, even layer. Bake for 14-16 minutes or until the cake springs back slightly when touched. Immediately remove parchment paper from the pan and place onto a clean, heatproof surface. Starting at the short end, gently roll the cake, with the parchment paper attached, and transfer rolled-up cake to cooling rack to cool completely.
While the cake cools, make the filling. Use a hand mixer or a stand mixer fitted with the whisk attachment to beat the whipping cream, cocoa powder, and espresso powder until stiff peaks form.
Once the cake has cooled to room temperature, carefully unroll. Spread the filling evenly over the cake. Re-roll, this time peeling the parchment paper off as you go. Chill in the refrigerator for 30 minutes before slicing and serving.
Notes
The cake must be completely cooled before you attempt to spread the filling on top, otherwise the filling will melt into your cake.