Cinnamon Swirl King Cake

About the recipe
This recipe is lightly adapted with permission from Anne Byrn’s cookbook, “American Cake,” where she writes that you can adapt the filling to suit any of your favorite flavors, such as raisins, chopped nuts, or even citrus zest.
Serves: 12 to 18
Hands On Time: 45 minutes
Total Time: 3 hours and 0 minutes
Ingredients
Dough
1/4 cup water, heated to 105 to 115 degrees
1/4 cup milk, heated to 105 to 115 degrees
2 1/4 teaspoons active dry yeast
8 tablespoons (1 stick), unsalted butter, sliced into thin pieces and softened, plus more for greasing the bowl
2 tablespoons granulated sugar
1/2 teaspoon ground nutmeg
1/2 teaspoon salt
3 cups all-purpose flour, plus more for kneading the dough
2 large eggs, lightly beaten
Filling
1 cup packed light brown sugar
2 teaspoons ground cinnamon
6 tablespoons unsalted butter, melted
Instructions
To make the dough: Lightly grease a large bowl with butter. Line a rimmed baking sheet with parchment paper.
In a second large bowl, stir together the water, milk and yeast. Stir in the butter, sugar, nutmeg and salt. Add 1 cup of the flour and blend well, smashing the butter against the sides of the bowl to mix it into the flour. Stir in the eggs and the remaining 2 cups flour. Mix well to form a soft dough.
Transfer the dough to a lightly floured counter and knead until the dough is smooth and elastic, about 5 minutes. Add a little more flour, if needed, to prevent the dough from sticking to the counter. Transfer to the buttered bowl. Turn the dough so that the top is greased. Cover with plastic wrap, place in a warm location, and let rise until the dough has doubled in size, 1 to 1 1/2 hours.
Meanwhile, make the filling: In a medium bowl, stir together the brown sugar and cinnamon.
Once the dough has risen, transfer it to a lightly floured counter and, with a floured rolling pin, roll the dough out to a 9- by 26-inch rectangle. Brush with the melted butter and sprinkle the brown sugar mixture evenly over the dough, leaving about 1/2 inch of bare dough along the far long edge.
Beginning at the long end closest to you, roll the dough up tightly, as for a jelly roll. Lightly blot the bare edge with water and press and pinch firmly to seal. Carefully pick up the rolled dough and place it, seam-side-down, on the prepared baking sheet. Bring together the two ends to make a 12-inch circle. Blot the ends with a little water and pinch together to seal. Use a sharp knife to slice open the middle of the circle all the way around, cutting through the layers and almost to the bottom of the dough. Cover with a clean kitchen towel, place in a warm location, and let rise until doubled in size, about 40 minutes.
Meanwhile, heat the oven to 350 degrees.
Once the dough has risen, bake until it is lightly browned all over, 25 to 30 minutes. Transfer the cake to a wire rack to cool for 15 minutes. If you’d like to insert a plastic baby figurine, push it into the underside of the cake now.
Slice and serve.