Combine the 1 cup milk, yeast, and the 1 teaspoon sugar in a small bowl and let stand until bubbly. Combine the flours, remaining sugar, raisins, candied peels, salt, and spices in a large mixing bowl and mix on low speed. Add the butter, 2 eggs, and the yeast mixture and continue to mix until a sticky dough forms -- about 3 minutes. Knead by hand on a floured surface for about 5 minutes. Form the dough into a ball and cover with a clean, damp kitchen towel and let rise in a warm place until it doubles in volume -- about 1 hour.
Line a baking pan with parchment paper and set aside. Punch the dough down, transfer and divide the dough into 12 equal-sized pieces.Shape each piece into a ball and place the balls about 1 inch apart in three rows of four on the prepared pan. Cover and let rise until the buns double in volume and touch one another -- about 1 1/4 hours.
Preheat oven to 400°F. Bake until golden brown -- about 20 minutes. Transfer to a wire rack. In a small bowl, combine the confectioners' sugar, milk, and vanilla in a bowl and stir until smooth.When buns have cooled slightly, drizzle a horizontal line across each row of buns followed by a vertical line to form a cross on the crown of each bun.