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Lightly grease a 10" square pan or 9" X 13" pan.
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Mix the rum or apple juice with the dried fruit and raisins, cover with plastic wrap and microwave briefly until the fruit and liquid are war.
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Set aside to cool to room temperature.
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When the fruit is cool, mix together all the dough ingredients except the fruit and knead, using an electric mixer or bread machine until the dough is soft and elastic.
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Mix in the fruit and any liquid not absorbed.
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Let the dough rise for 1 hour, covered. It will be puffy but may not necessarily double in bulk.
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Divide the dough into billiard, ball-sized pieces. Use your greased hands to round the dough into balls and arrange them in the prepared, greased pan.
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Cover the pan and let ht buns rise for 1 hour or until they've puffed up and are touching one another.
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While the dough is rising, preheat the oven to 375 (F) degrees.
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Whisk together the reserved egg white and milk and brush it over the buns.
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Bake the buns for 20 minutes until they are golden brown. Remove from the oven and allow to cool on a baking rack.
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Mix together the icing ingredients and when bus are cool, pipe the icing in a cross shape atop each bun.