Line the base of an 8-inch springform pan with parchment and lightly grease the sides. For clean layers later, add a tall parchment or acetate collar inside the rim.
Heat the oven to 340°F (171°C). In a heatproof cup, stir the espresso powder into the hot coffee and whisk in the sifted cocoa until smooth; set aside to cool to warm.
Whisk sugar, oil, vanilla, and sour cream in a large bowl until glossy. Beat in the eggs one at a time until the mixture looks slightly thickened and homogeneous.
Sift flour, baking powder, baking soda, and salt together. Add half of the dry mix to the wet bowl, stir just to combine, then add all the cocoa-coffee mixture. Add remaining dry mix and fold gently until no dry streaks remain; scrape the bowl bottom once to ensure it's evenly mixed.
Pour batter into the prepared springform and bake 30–35 minutes, until a tester in the center comes out with a few moist crumbs. Cool 10 minutes on a rack, then level the top if domed; keep the cake in the pan for assembly and let it cool to room temperature.
While the cake bakes, start the mousse: Sprinkle gelatin over 2 tablespoons of cold heavy cream in a small dish and let it hydrate for 3 minutes (it will look thick).
Melt the chopped chocolate in a heatproof bowl set over barely simmering water (double boiler), stirring until smooth. Microwave the bloomed gelatin for 5–7 seconds just to liquefy, then whisk it into the warm melted chocolate. Set aside to cool to lukewarm—no warmer than body temperature.
In a chilled bowl, whip 1 1/4 cups cold heavy cream to soft peaks; refrigerate briefly while you prepare the cream cheese base.
Beat cream cheese until completely smooth. Add powdered sugar, granulated sugar, cocoa, and vanilla; beat until velvety with no lumps. Mix in the melted chocolate-gelatin mixture until fully combined, scraping the bowl once. Fold in the whipped cream in two additions until the mousse is airy and uniform.
Spread the mousse over the cooled cake still in the springform, smoothing the top. Tap the pan gently to release air bubbles. Chill until just set, 45–60 minutes (or 20–25 minutes in the freezer).
For ganache, heat cream in a small saucepan until steaming with tiny bubbles around the edge. Pour over the chopped chocolate with a pinch of salt; let stand 2 minutes, then stir from the center outward until glossy. Cool to about 90–95°F—fluid but not hot.
Pour ganache over the set mousse and tilt the pan to coat evenly. Chill 20–30 minutes until the surface is softly set.
Optional finish: Whip 3/4 cup cold cream with powdered sugar, cocoa, and vanilla to medium-stiff peaks. Pipe rosettes around the edge. Refrigerate the cake at least 2 hours (or overnight) before unmolding and slicing.