1. Heat 1 cup milk in a small saucepan over medium heat until it registers 110 degrees on a candy thermometer. Pour milk into a mixer bowl, and fit mixer with a dough hook. With mixer on low speed, add granulated sugar, yeast, butter, 1 1/2 teaspoons salt, the nutmeg, cinnamon, and eggs. Add flour, 1 cup at a time, and knead until mixture comes together in a soft, sticky dough. Continue kneading, scraping down hook as needed, until dough is smooth, about 4 minutes.

2. Add cherries and raisins, and knead to incorporate. Turn dough onto a lightly floured surface, and knead to distribute dried fruit. Coat a large bowl with butter. Shape dough into a ball, and place in prepared bowl. Cover with a piece of plastic, and let rise until doubled in size, about 1 hour.

3. Generously butter a rimmed baking sheet. Turn dough onto a surface, knead briefly, then divide into 3 pieces. Working with 1 piece at a time, divide each third into 10 pieces, and shape each into a tight ball. (Keep dough covered with plastic.) Place on prepared sheet, spacing 1/2 inch apart. Repeat with remaining dough. Cover with plastic, and let rise in a warm spot until buns have doubled in size and are touching, about 1 hour.

4. Preheat oven to 375 degrees. Whisk together egg white and water in a small bowl. Brush tops of buns with egg-white wash. Bake, rotating sheet halfway through, until golden brown, 20 to 22 minutes. Let cool on sheet on wire rack for 30 minutes.

5. Whisk together remaining 3 tablespoons plus 2 teaspoons milk, confectioners' sugar, vanilla, and a pinch of salt. Spoon icing into a pastry bag fitted with a plain 1/4-inch round tip, and pipe icing on buns in the shape of a cross. (Alternatively, spoon glaze on buns.) Serve immediately.