Step 1: Bring 1 inch of water to a boil in a wide skillet. Reduce the heat to medium-low so the water is barely simmering. Pour the cream into a medium heat-resistant bowl, then place the bowl into the skillet. Heat the cream, stirring often, to 190 F. It will take about 15 minutes of delicate heating. Add the lime juice and continue heating the mixture, stirring gently, until the cream curdles. Do not expect the same action as you see during ricotta cheese making. All that the whipping cream will do is become thicker, like a well-done crème anglaise. It will cover a back of your wooden spoon thickly. You will see just a few clear whey streaks when you stir. Remove the bowl from the water and let cool for about 20 minutes.
Step 2: Meanwhile, line a sieve with four layers of dampened cheesecloth and set it over a bowl. Transfer the mixture into the lined sieve. Do not squeeze the cheese in the cheesecloth or press on its surface (be patient, it will firm up after refrigeration time). Once cooled completely, cover with plastic wrap and refrigerate (in the sieve) overnight or up to 24 hours.
Step 3: 2) CHOCOLATE GENOISE:
Preheat the oven to 350F. Line, grease & flour an 8-inch round cake pan. Sift the flour and cocoa together three times; reserve. Bring some water to a boil in a large pan/griddle & reduce to simmer. Place eggs & sugar in a large bowl, whisk constantly over the simmering water, heat the eggs to lukewarm (about 105F). Remove the bowl from the pan; leave the skillet on the stove but turn off the heat. With an electric mixer, beat the egg mixture at high speed until it has cooled, tripled in volume, and resembles softly whipped cream, about 5 minutes in a heavy-duty mixer or longer with a less powerful mixer.
Step 4: Meanwhile, set the bowl of clarified butter/ghee and vanilla in the skillet of hot water, with the burner off, to keep it warm. Sift about one-third of the flour and cocoa over the whipped eggs. Use a rubber spatula to fold in the mixture-quickly but gently-until combined. Fold in half the remaining flour and cocoa, then fold in the rest. Remove the warm butter mixture from the skillet. Scoop about 1 cup of the batter into the bowl with the butter and fold together until completely combined. Use the large rubber spatula to fold the butter mixture completely into the remaining batter. Turn the batter into the prepared pan and tilt to level.
Step 5: Bake until the cake beginning to shrink slightly around the edges and the top springs back when pressed with your finger, about 40-45 minutes. Cool the cake completely in the pan on a rack. To unmold, run a small knife or spatula around the inner edges of the pan. Invert it onto a rack and remove the parchment liner. Turn the cake right side up. The génoise can be wrapped and refrigerated for up to 2 days, or frozen for up to 3 months.
Step 6: 3) MOCHA MASCARPONE FROSTING:
Beat mascarpone cheese with a wooden spoon till smooth. Fold in the rest of the ingredients & mix with the spoon till smooth.
Step 7: To assemble:
Make a strong coffee syrup with 1/4 cup of hot water, 2-3 tsps sugar & 2 tsps coffee powder. Cool.
Cut the genoise into 2 horizontal layers. Place one layer on the cake platter. Brush well with the coffee syrup. Sandwich with a little less than half the mocha mascarpone. Top with the second layer, & brush that well with the coffee syrup. Frost the top & sides of the cake with the remaining mascarpone. Grate dark chocolate over the top, edge with coffee beans, & sift cocoa over the edges. Chill for 3-4 hours.