Make the cake: In a large measuring cup, stir the slightly hot water and 1 tablespoon of the sugar together, then stir in the yeast. Let the mixture sit for 10 minutes until bubbling and foamy.
In the bowl of a stand mixer, whisk together the flour, cinnamon, nutmeg, remaining ⅓ cup (67 g) sugar, and salt in a large bowl. Snap on the dough hook and turn the speed on to low. Pour in the yeast mixture and beat to incorporate. Beat in the buttermilk. Add the eggs, one at a time, beating well after each addition. Add the butter and let the dough knead until it comes together, about 2 minutes. Bump up the speed to medium and let the dough knead for a final 4 minutes.
Transfer to a large greased bowl and cover with plastic wrap. Let the dough sit in a warm dark place to rise and double in size, about 2 hours.
Punch the dough down and let it rest for 5 minutes. Line a 13 × 18-inch (33 × 46 cm) baking sheet with parchment paper. Transfer the dough to a lightly floured work surface and roll it out into a smooth rope 28 inches (70 cm) long. Form the dough rope into an oval on the lined baking sheet, then grab one end and use it to enclose the second end, pinching any seams to close. If you are hiding a plastic baby, press it into the dough at this time, making sure to pinch any seams closed.
Let the dough rest in a dark and warm place until doubled in size, 45 minutes to 1 hour.