Cinnamon Roll Cake with Cream Cheese Frosting

To prepare dough: Combine 1 cup warmed milk, granulated sugar and yeast in a stand mixer. Let stand until the yeast starts to dissolve and foam, about 5 minutes. Whisk in egg and 4 tablespoons melted butter. Add whole-wheat flour, all-purpose flour and salt. Mix with a dough hook at medium speed until the dough comes together and starts to pull away from the sides of the bowl. (The dough will seem wet.) Cover with a kitchen towel and let stand in a warm place until risen slightly, about 1 hour.

To prepare filling and assemble cake: Combine brown sugar, melted butter and cinnamon in a small bowl.

Coat a 9-inch round cake pan with cooking spray. Turn the dough out onto a lightly floured surface. Roll out into an 18-by-10-inch rectangle. Spread the filling over the dough, leaving a 1-inch border on the short ends. Cut the dough into 10 equal strips, each about 1 3/4 inches wide. Starting at a short end, roll one strip into a round. Place the rolled dough at the bottom of another strip and roll the second strip around the first. Repeat with the remaining strips. If the last few strips become too hard to roll, place the cake in the center of the prepared pan and wrap the remaining strips around the outside of the roll. (It should look like a giant cinnamon roll!) Cover and let rise in a warm place until it almost meets the sides of the pan, about 30 minutes.

Preheat oven to 350 degrees F. Bake the cake until golden and a toothpick inserted in the center comes out clean, 25 to 30 minutes. Let cool slightly, then transfer the cake to a serving platter.

Meanwhile, prepare icing: Combine cream cheese, confectioners' sugar and vanilla in a stand mixer fitted with the paddle attachment. Beat on medium speed, scraping down the sides as needed, until creamy. Add milk and continue beating until combined. While the cake is still warm, drizzle the icing over the top. Serve warm.