Combine 2 1/2 cups flour, sugar, and next 4 ingredients in the mixing bowl of a heavy-duty stand mixer, stirring well. Set aside.
Combine milk, 1/4 cup water, and butter pieces in a saucepan; cook over medium heat, stirring constantly, just until butter melts. Cool 5 minutes (to 130°).
Pour milk mixture into flour mixture, and beat at low speed with dough hook attachment 2 minutes or until dry ingredients are moistened. Increase speed to medium; add eggs, 1 at a time, beating just until yellow disappears after each addition. Beat 3 more minutes. Reduce speed to low, and gradually beat in enough remaining flour (up to 2 1/2 cups) to make a soft dough (dough will be sticky). Beat at medium speed with dough hook attachment 5 minutes.
Scrape dough into a large bowl coated with cooking spray, and lightly spray the top of the dough.
Cover and let rise in a warm place (85°), free from drafts, 1 hour. (Dough will almost double in bulk.)
Punch dough down, and turn out onto a floured surface. Combine 2/3 cup currants, 1/3 cup raisins, and 1 Tbsp. flour, stirring to coat. Knead about one-fourth of fruit mixture at a time into dough until all fruit mixture is evenly dispersed.
Divide dough into 20 equal portions; shape each portion into a 2-inch ball. Evenly space dough balls on a parchment paper-lined 15- x 10-inch jelly-roll pan; cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk. Gently brush tops with beaten egg white.
Bake at 375° for 15 minutes or until buns are a deep golden brown and sound hollow when tapped. Cool buns 15 minutes in pan on a wire rack.
Spoon icing into a zip-top plastic freezer bag; snip a 1/4-inch piece from corner of bag, and pipe an "X" on top of warm buns, forming a cross. Serve remaining icing with buns, if desired.
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