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1
Preheat the oven on 375u00b0F.
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2
Combine milk and black sugar in a sauce pot and set it over low heat. Simmer until the sugar has completely dissolved. The milk may start to curdle. Let the milk cool down slightly, then whisk in the yogurt. Let the mixture cool down to room temperature.
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3
Combine the dried longan and rum in a bowl, and heat it in the microwave for 40 sec. Mix well and let the longan soak and plump up in the hot rum for 20 min.
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4
Sift flour, baking powder, baking soda and salt together. In a mixer with a fitted pedal, cream the butter and granulated sugar for 5 min until pale and fluffy. Add the eggs 1 at a time. Then add 1/3 of the flour mixture, and mix for 5 sec. Then 1/2 of the milk mixture, and mix for another 5 sec. Then another 1/3 of the flour mixture, followed by the last 1/2 of the milk mixture, and finally the last 1/3 of the flour mixture. Mix for 5 seconds in between and every time you stop, scrape the sides and bottom of the bowl so everything is mixed evenly. Add the soaked longan and rum, mix until just combined.
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5
Line a round cake pan with parchment paper, and pour the batter into the pan. Smooth the top with a spatula and bake in the 375u00b0F oven for 25 min. Then lower the temperature down to 350u00b0F, and bake for another 25 minutes. Let the cake cool on a rack and make the icing.
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6
Melt 4 tbsp of unsalted butter in a pot over medium heat. Let the butter sizzle and bubble. When the sizzling sound starts to subside, you'll see the milk solids nicely browned and the butter turns dark and nutty, approx 5~7 min. Strain the browned butter through a fine sieve into a bowl. Add the powder sugar and whisk, then gradually add in the milk until it reaches a desired consistency. Add the vanilla extract and whisk until smooth.
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7
Smear the icing on top of the cake.
