Preheat oven to 325°F (160°C). Liberally grease a 10″ round pan with vegetable shortening. Cut out a 10″ round of parchment paper, using bottom of pan as a template. Place inside pan, smoothing it out to cling securely to the shortening.

Combine melted butter, flour, brown sugar, and rum in a small saucepan. Heat on low, stirring until well combined. Pour into prepared cake pan, spreading evenly. Arrange mango slices on top of this mixture, set aside.

Combine flour, sugar, baking powder, salt, and pudding mix in a large mixing bowl. Add in eggs and rum beating until smooth. Carefully add mango pulp and melted butter to the mix, mixing on medium speed until smooth. Carefully pour into prepared pan. Bake until golden and knife inserted into center of batter comes out clean and cake springs back – about 50-60 minutes.

While cake is baking, combine butter, water, mint leaves, sugar, and rum in a small saucepan. Allow to heat to a simmer, then remove from heat and allow to cool. Once cool, strain – pressing trapped liquid out of the mint. Discard mint leaves, set syrup aside.

With the hot cake still in the pan, carefully level the top by cutting off the “dome” over the edge of the pan. Evenly pour the mint syrup over the entire cake. Allow cake to cool for about 20 minutes before turning cake out directly onto serving plate. This cake is delicate, and should not be moved to a different plate after being turned out!

While cake is cooling on serving plate, Heat ¼ cup amber rum. Add mint leaves, and let steep for 10 minutes. Strain, once again pressing trapped liquid out of the mint. Discard mint leaves. Mix as much icing sugar into the ¼ cup rum as it takes to make a very thick paste. Melt it in the microwave for a few seconds, then drizzle over the cake. If desired, stir a tiny drop of green food coloring into the frosting before drizzling – pale mint green drizzle looks pretty on this cake!

Garnish with sprigs of fresh mint, if desired.