In a measuring cup, combine the warm water, 1 tablespoon of granulated sugar, and the warm milk. Stir in the yeast and allow the mixture to sit for approximately 10 minutes, or until it becomes foamy.

In a large mixing bowl, whisk together the flour, salt, grated nutmeg, cinnamon, and lemon zest. Set aside.

Using a stand mixer fitted with the paddle attachment, cream the softened butter and the remaining 1/2 cup of granulated sugar until the mixture is light and fluffy. Beat in the egg yolks one at a time, ensuring they are fully incorporated.

Gradually add the flour mixture to the creamed butter and eggs. Once it begins to resemble coarse crumbs, pour in the yeast mixture. Mix until a dough begins to form.

Switch to the dough hook attachment and knead the dough on medium-low speed for 5 to 8 minutes, or until the dough is smooth and begins to pull away from the sides of the bowl. If the dough is too sticky, add additional flour one tablespoon at a time as needed.

Transfer the dough to a lightly oiled bowl. Cover with plastic wrap or a clean towel, and allow it to rise in a warm area for approximately 2 hours or until it has doubled in volume.

Punch down the dough and turn it onto a lightly floured surface. Let it rest for 10 minutes. Then roll it into a 16×21-inch rectangle. Spread the surface evenly with the softened butter. In a small bowl, mix the brown sugar and cinnamon, then sprinkle the mixture over the buttered dough. Place the plastic baby somewhere on the dough.

Starting from the long edge, roll the dough tightly into a cylinder. Pinch the seam to seal. Shape the dough into a ring and place it seam-side down on a parchment-lined baking sheet. Insert a greased coffee can or heat-safe jar in the center to help maintain a circular shape. Cover loosely and let it rise for an additional 45 minutes, or until puffy.

Preheat the oven to 350°F (175°C). In a small bowl, whisk together the egg white and 1 tablespoon of milk. Brush the top of the risen dough with this mixture. Bake the cake for 35 to 40 minutes, or until golden brown and an internal thermometer reads 200°F to 210°F. Transfer to a wire rack and let cool completely before icing.

In a mixing bowl, beat the confectioners’ sugar and softened butter until smooth. Add the lemon juice and lemon zest and mix until combined. Adjust thickness with more sugar or juice if necessary.

Drizzle or pipe the lemon icing over the cooled cake. Immediately sprinkle with alternating bands of purple, green, and gold sugars. Allow the icing to set before slicing and serving.