Combine the warm whole milk, the granulated sugar (for dough), and the active dry yeast in a large bowl; whisk and let stand until foamy, 5–10 minutes.
In a separate bowl, whisk together the all-purpose flour (4 cups), kosher salt, ground cinnamon, ground allspice, ground nutmeg, and orange zest.
Add the unsalted butter and the large egg to the foamy yeast mixture, then add the dry ingredients; stir with a wooden spoon until a shaggy dough forms.
Turn the dough out onto a work surface lightly dusted with the all-purpose flour (for dusting) and knead until smooth and elastic, 8–10 minutes.
Flatten the dough and scatter over the currants, raisins, and candied citrus peel; knead gently just until evenly distributed, 1–2 minutes.
Shape the dough into a ball, lightly grease a clean bowl with the neutral oil, place the dough seam-side down, cover, and let rise in a warm spot until doubled, 60–90 minutes.
Punch down the dough, divide into 12 equal pieces, and shape each into a tight ball. Arrange on a parchment-lined sheet pan (3 by 4) or in a 9×13-inch pan so they will just touch as they rise. Cover and let rise until puffy and touching, 45–60 minutes.
Preheat the oven to 375°F (190°C). Mix the all-purpose flour (for cross paste) with the water (for cross paste) to make a thick, pipeable paste; transfer to a small piping or zip-top bag and snip a tiny corner.
Pipe a continuous line across each row of buns, then another line at right angles to form crosses.
Bake until deep golden brown and the buns sound hollow when tapped on the bottom, 18–22 minutes; an instant-read thermometer should read about 200°F (93°C).
While the buns bake, combine the granulated sugar (for glaze) and the water (for glaze) in a small saucepan and simmer over medium heat until the sugar dissolves, 1–2 minutes.
Brush the hot buns with the warm syrup, then cool on a rack for 15 minutes before serving.