Step 1: In a large bowl, combine the warm milk, 1 tablespoon of the granulated sugar, and the instant yeast. Stir gently and let sit for 5 minutes until slightly frothy. (If using active dry yeast, proof as described in the Key Ingredient Notes section).
Step 2: In a separate large bowl, whisk together the bread flour, remaining granulated sugar, salt, cinnamon, nutmeg, and allspice.
Step 3: Add the melted butter and beaten egg to the yeast mixture. Gradually add the dry ingredients to the wet ingredients, mixing with a wooden spoon or stand mixer with a dough hook until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for 8-10 minutes (or 5-7 minutes in a stand mixer) until it's smooth, elastic, and passes the windowpane test.
Step 4: Flatten the dough slightly and spread the soaked and drained dried fruit over it. Fold the dough over and knead gently for another 1-2 minutes until the fruit is evenly distributed.
Step 5: Place the dough in a lightly oiled bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 1.5 hours, or until doubled in size.
Step 6: Gently punch down the dough to release the air. Turn it out onto a lightly floured surface and divide it into 12 equal pieces (approximately 70-75g each). Roll each piece into a smooth, round ball. Arrange the buns on a baking sheet lined with parchment paper, leaving a little space between them.
Step 7: Cover the baking sheet loosely with plastic wrap or a clean towel and let the buns rise again in a warm place for another 45-60 minutes, or until they have nearly doubled in size and are puffy.
Step 8: While the buns are proofing for the second time, prepare the cross mixture: In a small bowl, whisk together 1/2 cup all-purpose flour and 4-5 tablespoons cold water until a smooth, thick paste forms. Transfer this paste to a piping bag with a small round tip, or a ziplock bag with a tiny corner snipped off. Once the buns are proofed, carefully pipe a cross shape onto the top of each bun.
Step 9: Preheat your oven to 375°F (190°C). Bake the buns for 20-25 minutes, or until they are golden brown and sound hollow when tapped on the bottom.
Step 10: While the buns are baking, prepare the glaze: Gently heat the apricot jam with 1 tablespoon of water in a small saucepan or microwave-safe bowl until it's liquid and brushable. As soon as the buns come out of the oven, generously brush them with the warm glaze. Let them cool slightly on a wire rack before serving.