Line the bottom of an 8-inch springform pan with parchment and lightly grease the sides. For extra clean edges later, line the sides with a strip of parchment or an acetate collar. Preheat the oven to 325°F (165°C).
Whisk the hot coffee and instant espresso powder together, then whisk in the cocoa powder until smooth and glossy. Set aside to cool slightly while you start the batter.
In a large bowl, beat the sugar, eggs, and vanilla for 1 minute until lightly foamy. Slowly stream in the oil while whisking to emulsify.
In a separate bowl, sift the flour with the baking powder, baking soda, and salt. Fold half of this dry mix into the egg mixture, then whisk in the cocoa–coffee slurry and the Greek yogurt. Add the remaining dry mix and stir just until no dry streaks remain.
Scrape the batter into the prepared springform. Bake at 325°F for 32–38 minutes, until the center springs back and a toothpick comes out with a few moist crumbs. Cool 15 minutes in the pan, then level the top if domed. Keep the cake in the springform and chill it in the freezer for 10 minutes to firm while you begin the mousse.
Bloom the gelatin: sprinkle it over the cold water in a small bowl and let stand 5 minutes. Meanwhile, place the chopped chocolate in a heatproof bowl set over a pan of barely simmering water (do not let the bowl touch the water) and stir until melted and smooth. Remove from heat to cool for 5 minutes.
In a chilled bowl, whip 1 cup (240ml) of the heavy cream to soft peaks; refrigerate. In another bowl, beat the cream cheese, powdered sugar, vanilla, and a pinch of sea salt until creamy and lump-free, 1–2 minutes.
Liquefy the bloomed gelatin by warming it briefly (5–8 seconds in the microwave, or set the bowl in warm water) until just melted. Whisk the liquid gelatin into the melted chocolate until glossy and uniform.
Blend the chocolate–gelatin mixture into the cream cheese base until fully combined. Fold in the whipped cream in two additions, keeping the mixture airy. If it feels loose, refrigerate the bowl for 5 minutes to slightly thicken before assembling.
Spoon the mousse over the cooled cake in the springform. Smooth the top and tap the pan gently on the counter to release any large air bubbles. Cover and refrigerate until set, 1½–3 hours.
Make the ganache: heat the cream in a small saucepan just to a simmer. Pour over the chopped chocolate in a bowl, let stand 1–2 minutes, then stir from the center out until smooth. Cool 10–15 minutes until thickened but still pourable, then spread over the set mousse. Chill 20–30 minutes to lightly set the glaze.
For the topping, whip the remaining 1/4 cup (60ml) heavy cream with the powdered sugar and vanilla to medium peaks. Pipe rosettes or a simple border around the edge. To serve, warm a thin knife under hot water, wipe dry, and cut clean slices.