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In a medium sized bowl, dissolve the yeast with the warm water.
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Add the sugar and one of the eggs and whisk to combine.
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Mix in 1 1/2 cups of flour until the batter is smooth and sticky.
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Cover with a towel and let it rest for 30 minutes.
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After 30 minutes add the oil and salt. Mix well with a spatula.
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Add the coconut and remaining 1 cup of flour to the batter and mix until the dough starts to come together.
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Dump the dough out onto a clean work surface which has been dusted with more flour.
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The dough will be sticky but start to fold it over on itself and kneading it at the same time. Add more flour if it becomes too sticky.
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When you finally form a round ball, put it back into the bowl it was mixed in and cover for 35-40 minutes.
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Take the dough out of the bowl after the second rise and punch the air out of it.
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divide the dough into 12 even sized pieces (about 2 oz each).
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Roll the dough pieces into small bowls and place close together on a greased baking tray in a 3 x 4 pattern.
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Cover with the towel again and let rise for about 20 minutes.
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Preheat the oven to 375 degrees F.
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Once the rolls have risen after 20 minutes, using a pastry brush gently glaze them with the remaining beaten egg.
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Place them in the oven and bake for 20 minutes.
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Let the buns cool while you make the icing.
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Add the powdered sugar to a bowl and mix in the water using a whisk. The icing will seem thick but keep whisking until it becomes smooth and lump free.
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Once the buns are cool, dip each one into the icing and letting the excess pour off.
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Transfer back to the baking tray until every bun has been iced.