Mixing and storing the dough: Mix the water, yeast, salt, eggs, honey, and melted butter in a 6-quart bowl, lidded (not airtight) food container, or the bowl of a stand mixer.
Mix in the flour, spices, zest, vanilla, and raisins without kneading, using a spoon or heavy-duty stand mixer (with paddle). If you’re not using a machine, you may need to use wet hands to incorporate the last bit of flour. The dough will be loose but will firm up when chilled; don’t try to work with it before chilling.
Cover (not airtight), and allow to rest at room temperature for 2 hours, then refrigerate.
The dough can be used as soon as it’s thoroughly chilled, at least 3 hours. Refrigerate the container and use over the next 5 days.
On baking day: Dust the surface of the refrigerated dough with flour and cut off a 2-pound (907g, cantaloupe-sized) piece. Divide the dough into 8 or 9 equal pieces and quickly shape into balls.
Place 2 inches apart on a baking sheet lined with parchment paper or silicone mat, cover loosely with plastic wrap and allow to rest at room temperature for about 45 minutes.
Preheat the oven to 350°F, with a rack placed in the center of the oven.
Brush the tops of the risen buns with the egg wash and place the baking sheet in the oven. Bake for about 25 minutes, or until richly browned.
Allow to cool completely on wire rack. Pipe the icing in a cross over the top of each bun. There will be some extra icing for spreading on the buns.
To make the icing: Mix the cream cheese, butter, confectioners’ sugar, and maple syrup in a small bowl until smooth.