For the dough: Melt the butter in a small saucepan over low heat. Remove from the heat and pour in the milk and water. The mixture should be just warm to the touch, about 110 degrees F; let cool or heat over low heat as needed. Stir in the yeast and let stand for 5 minutes, until bubbles come to the surface.
In a large bowl, whisk together the flour, salt, cinnamon and nutmeg.
In a small bowl, stir together the brown sugar, orange zest and egg yolks. Whisk in the yeast mixture. Add the liquid mixture to the dry ingredients; fold with a rubber spatula until all the flour is incorporated and a slightly sticky dough forms.
Turn the dough out onto a floured work surface and sprinkle the top with flour. Knead for 2 to 3 minutes, until the dough becomes smooth and no longer sticks to the work surface. Lightly grease a medium bowl with the canola oil and add the dough, turning to coat. Cover the bowl and let proof in a warm place until doubled in size, about 1 hour.
For the filling: Add the cream cheese, confectioners' sugar, orange juice, cinnamon, salt and nutmeg to a medium bowl. Mix with a hand-held mixer or rubber spatula until completely combined and smooth. Set aside.
Bake the cake: Preheat the oven to 350 degrees F. Line a rimmed baking sheet with parchment.
Remove the proofed dough to a lightly floured work surface and roll into an 8-by-28-inch rectangle, about 1/4-inch thick. Spread evenly with the cream cheese filling, leaving a 2-inch border. Add the plastic baby to the filling, and then roll the dough into a 28-inch log. With the log seam-side down, bring both ends together to form a circle. Lightly brush the inside of one end with water and insert the other end inside to close the circle. Brush the seam lightly with water and pinch to seal. Place the dough onto the prepared baking sheet, making sure to form it back into a circle--it should be approximately 10-inches in diameter. Using a paring knife, make six 2- to 3-inch diagonal slits in the top of the dough (to act as vents during baking). Let the dough rise an additional 30 minutes, until puffed up and the vents have opened slightly.
Bake the cake for 40 minutes, until the top and bottom have a deep golden-brown crust. The slits may also widen as during baking; that is normal. Remove the cake from oven and let cool for 30 minutes on the baking sheet.
For the icing: Whisk together the confectioners' sugar, milk and orange juice until smooth. Spoon the icing over the top of the cooled cake, pushing it to either side. If some icing pools in the center or on the sides, just scoop it up and drizzle it over the cake again; you want to make sure the entire cake is covered in icing. Working quickly, so the icing doesn't set, sprinkle the yellow sanding sugar over a 2-inch section of the cake. Next to that, sprinkle the green sanding sugar, followed by the purple. Continue in this pattern until the entire cake is covered in sanding sugar.
Transfer the cake to a cake stand and serve immediately, or hold at room temperature until ready to serve. This cake is best served the same day.