In the bowl of a stand mixer, whisk together 3¼ cups flour, sugar, yeast, salt, and nutmeg. Add the milk, butter, eggs, and vanilla. Using the dough hook attachment, mix on medium-low speed until a smooth and sticky dough forms, about 15 minutes, scraping down the bowl a few times throughout mixing. The dough will be loose, almost like a stretchy cake batter. It should feel tacky but not stick to a clean finger when quickly touched. Add the remaining ¼ cup of flour if the dough is sticking to your finger after 15 minutes. Scrape the dough down into the bowl, cover, and let rise in a warm spot until doubled in size, about 1 hour.

On a lightly floured work surface, turn out the risen dough. Roll and stretch the dough into a 10x20-inch rectangle. Let it rest while you make the filling.

In a small bowl, combine brown sugar, cinnamon, and butter, stirring until well combined. Spread the filling over the dough, leaving a ½-inch border on one long side.

Starting at the long side opposite the border, tightly roll up the dough into a log, pinching the seam to seal. Roll seam side down. Carefully transfer to a piece of parchment paper. Bring the two ends together to form a wreath, and pinch the ends together to create a wreath.

Place the wreath with the parchment paper on a rimmed baking sheet, reshaping the wreath into a circle, if needed. With scissors, cut the edge of the dough to allow expansion and prevent cracking as the dough rises. Loosely cover and let rise until doubled in size, 45 minutes to 1 hour.

While rising, preheat the oven to 350F.

When risen, use a sharp knife or kitchen shears to make cuts about a third of the way through, spaced 1 inch apart all around the outside of the dough ring.

Uncover and bake for 25 to 30 minutes or until golden brown. Let cool completely on the pan. Transfer to a serving platter.

In a small bowl, whisk together confectioners’ sugar and milk until thick but spoonable. Spoon over the top of the cake, using the spoon to cover the top, and push the icing to drip down the sides. Decorate with alternating sections of green, purple, and yellow sugars.