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Combine warm milk, yeast, and a pinch of sugar in a bowl. Let sit for 5 to 10 minutes until foamy.
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Add the remaining sugar, softened butter, and egg to the yeast mixture. Stir to combine.
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In a large bowl, whisk together flour, salt, cinnamon, nutmeg, and allspice. Add the wet ingredients and stir until a shaggy dough forms.
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Turn out onto a floured surface and knead for 8 to 10 minutes until smooth and elastic. Knead in the orange zest and currants during the last minute.
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Place in a greased bowl, cover with a towel, and let rise for about 1 hour until doubled in size.
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Punch down the dough and divide into 12 equal pieces. Shape each into a smooth ball and arrange in a greased 9x13 baking dish. Cover and let rise for 30 to 40 minutes until puffy.
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Preheat oven to 375 degrees F. Bake for 18 to 20 minutes until golden brown.
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Brush the hot buns with honey immediately out of the oven.
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Mix powdered sugar and milk to make a thick icing. Pipe crosses on top of each bun once they have cooled slightly.