Position a rack in the center of the oven and preheat to 350°F. Line a 9x13-inch baking pan with parchment, letting the paper hang over two short sides for easy removal.
In a large bowl whisk together the granulated sugar, brown sugar, oil, milk, cooled coffee, eggs and vanilla until smooth and slightly glossy (about 1 minute by hand or 30 seconds with a mixer).
In a separate bowl sift (or whisk) the flour, cocoa powder, baking soda, baking powder, salt and instant espresso powder until evenly combined.
Add the dry ingredients to the wet in two additions, folding gently with a rubber spatula until just combined. The batter will be fairly loose; scrape it into the prepared pan and smooth the top.
Bake for 36–40 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs. Begin making the ganache while the cake bakes.
To make the ganache: place the chopped chocolate in a heatproof bowl. Heat the cream in a small saucepan until it just begins to simmer at the edges, then pour it over the chocolate. Let sit 1 minute, then stir until smooth. Set aside about 3 tablespoons for drizzling later and keep the rest warm.
When the cake comes out of the oven, immediately use the handle of a wooden spoon (or a chopstick) to poke holes evenly across the surface, about 1 inch apart. Pour most of the warm ganache over the hot cake, concentrating on filling the holes so the sauce sinks into the crumb. Reserve the pan on a wire rack to cool to room temperature.
Chill a mixing bowl and beaters for at least 5 minutes. Pour the cold heavy cream and sifted powdered sugar into the chilled bowl and whip on medium-high until the cream holds soft peaks.
Add chilled mascarpone, sifted cocoa, vanilla and the pinch of salt to the whipped cream and beat just until the mixture is smooth and reaches a light, pipeable consistency—stop at medium peaks to avoid splitting.
Once the cake is fully cooled, spread the mascarpone-cocoa whipped topping in an even layer (or pipe decorative swirls). Drizzle the reserved ganache over the top and chill 20–30 minutes to set the topping before slicing into 12 pieces.
Serve chilled or at cool room temperature. Store leftovers covered in the refrigerator for up to 3 days.