In a stand mixer fitted with the whisk attachment, beat the eggs on medium speed, gradually adding the granulated and brown sugars. Continue beating for about 8 minutes, until pale and fluffy.

Add the oil and whisk to combine. Add the self-rising flour, instant coffee and water, mixing until smooth.

For the chocolate batter, combine the dark chocolate and non-dairy whipping cream in a microwave-safe bowl. Microwave in short intervals, stirring between each, until melted and smooth. Stir in ½ cup of the cake batter.

Pour the cake batter into the prepared pan. Drizzle the chocolate batter over the top in rows, then swirl with an offset spatula to create a marble pattern.

Bake for about 40 minutes, until a toothpick inserted into the center comes out with moist crumbs. Let the cake cool completely in the pan.

For the topping, beat the non-dairy whipping cream in a stand mixer until it begins to thicken. Add the vanilla instant pudding mix and beat until firm.

Spread the cream evenly over the cooled cake and sprinkle with the grated chocolate.