Coat a large bowl with non-stick spray and set aside.
In a food processor, combine ¼ cup of the flour with the candied lemon and orange peel. Pulse until finely minced. Transfer the mixture to a large bowl, then stir in the remaining 3¾ cups of flour, along with the salt, cinnamon, nutmeg, and allspice.
Heat milk and sugar in a saucepan over medium heat until the sugar dissolves. Off the heat, add butter and stir until melted. When the mixture is between 110-115°F (43-46°C), whisk in yeast and let stand for 5-10 minutes, or until bubbly. Transfer to the bowl of a stand mixer.
Add beaten eggs and flour to the yeast mixture and knead with the dough hook attachment on medium-low speed. Add currants and knead until incorporated.
Transfer the dough onto a floured surface and knead the dough until smooth. Shape into a ball and place in the prepared bowl. Cover and let dough rise in a warm place until it has doubled in size, about 2 hours.
Punch down dough and cut into 18 equal pieces, about 2½ ounces (70g) each. Shape dough into buns and place on a parchment-lined baking sheet. Spray buns with non-stick spray and lightly cover with plastic wrap . Let buns rest until doubled in size, about 2 hours.
Preheat oven to 375°F (190°C). Whisk together 1 egg and 1 tablespoon of milk. Brush the buns with the egg wash, then bake until golden brown, about 20 minutes.