Preheat your oven to 350°F (180°C). Line a 8-inch (20 cm) cake pan with parchment paper.
In a heatproof bowl set over a simmering pot of water (double boiler), melt the milk chocolate and butter together. Let it cool slightly.
In a separate bowl, whisk the eggs and sugar together until light and fluffy.
Add the rum and the cooled chocolate-butter mixture to the egg mixture, and mix thoroughly.
In another bowl, whisk together the flour, baking powder, and salt. Gradually sift the dry ingredients into the wet ingredients, gently folding until just combined. Be careful not to overmix.
Pour the batter into the prepared cake pan and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before removing it to a wire rack to cool completely. Before serving, garnish with grated chocolate or powdered sugar, if desired.
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