Preheat the oven to 340°F (170°C) with convection, if available. Line two baking sheets with parchment paper and lightly grease both the pans and parchment.
In the bowl of a stand mixer fitted with the whisk attachment (or using a hand mixer), beat the eggs with a pinch of salt on medium speed. Gradually add the sugar and continue beating until the mixture is pale, airy, and tripled in volume. Sift in the flour and baking powder, then gently fold until the batter is smooth and free of lumps.
Divide the batter evenly between the prepared pans and spread with an offset spatula to smooth the tops. Bake for about 13 minutes, until lightly golden and springy to the touch. Let cool completely.
Once cool, remove the cakes from the parchment. Cut one round that is 2 inches/5 cm larger than your dome mold. Line the mold with plastic wrap, then press the large cake round into the mold, trimming it to fit snugly. Cut another round to match the mold’s diameter. Reserve all cake trimmings for layering.
In a clean mixing bowl, whip the cream, sugar, and mascarpone until thickened. Add the vanilla pudding powder and beat until stiff peaks form. Transfer one-third of the cream to a separate bowl. Fold in the dulce de leche and toasted coconut until combined.
Spread one-third of the plain cream into the cake-lined mold. Top with an even layer of cake scraps. Spread the dulce de leche coconut cream over that, smoothing with an offset spatula. Add another layer of cake scraps or the smaller cake round. Finish with the remaining plain cream and smooth the surface. Place the final cake round on top to seal. Cover with plastic wrap and refrigerate for at least 3 hours.
Place the milk chocolate, dark chocolate, and oil in a microwave-safe bowl. Heat in short bursts, stirring between each, until fully melted and smooth.
Remove the cake from the mold and unwrap it. Set it on a wire rack positioned over a parchment-lined sheet pan. Pour the melted chocolate glaze evenly over the cake, letting the excess drip off. Drizzle with additional dulce de leche and sprinkle with toasted coconut.
Refrigerate until the glaze is set. Slice and serve chilled.