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Grease a large bowl and set aside. Grease 2 baking sheets or line them with parchment or non-stick liners.
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Whisk together 2 cups flour, yeast, sugar, salt, cinnamon, nutmeg, ginger, and cardamom in the bowl of a stand mixer.
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Heat water and butter in a small saucepan until warm, 120-130 degrees F (butter does not need to melt). Add to flour mixture.
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Lightly beat eggs and add to flour mixture.
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Blend at low speed using the flat beater until moistened.
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Change flat beater to dough hook and turn mixer to recommended setting for the dough hook.
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Gradually add currants and enough flour to make a soft dough (it should "clean" the side of the bowl). Knead with mixer/dough hook for 5 minutes.
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Transfer dough to a lightly floured surface and hand knead a few times.
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Place dough in greased bowl, turning to grease top. Cover and let rise in a warm place until double, about 1 hour.
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Punch dough down and transfer to a lightly floured surface. Roll dough to 1/2-inch thickness.
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Cut out buns with a 2- to 2 1/2-inch round cutter.
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Place cut-out rounds 1 1/2-inches apart on baking sheets. Cover and let rise in a warm place until double, about 30 minutes.
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Preheat oven to 350 degrees while buns are on the second rise.
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Gently brush tops with egg white. Bake for 12 to 15 minutes or until golden brown.
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Remove buns from cookie sheets. Serve warm.