Follow these detailed step-by-step instructions carefully to ensure your Sweet Cream Cheese Swirls come out perfectly tender, flavorful, and beautiful every time. Baking is a science, and each step plays a crucial role in the final outcome.

Part 1: Making the Enriched Dough

1. Activate the Yeast: In the bowl of a stand mixer fitted with the dough hook, or in a large mixing bowl, combine the warm milk, granulated sugar, and instant yeast. Give it a gentle whisk and let it sit for 5-10 minutes. The mixture should become foamy and bubbly. This process, called “blooming,” confirms your yeast is alive and active. If it doesn’t foam, your yeast may be expired, and you should start over.
2. Combine Wet Ingredients: Once the yeast is foamy, add the room temperature egg, melted and cooled butter, and vanilla extract to the bowl. Whisk lightly to combine everything.
3. Add Dry Ingredients and Mix: Add the all-purpose flour and salt to the wet ingredients in the bowl. Turn the mixer on to a low speed and mix until a shaggy, rough dough begins to form. Scrape down the sides of the bowl as needed to incorporate all the flour.
4. Knead the Dough: Increase the mixer speed to medium-low and knead the dough for 7-9 minutes. The dough should transform from a shaggy mess into a smooth, elastic, and slightly tacky ball. It should pull away cleanly from the sides of the bowl. If kneading by hand, turn the dough out onto a lightly floured surface and knead vigorously for 10-12 minutes until it becomes smooth and elastic. To check if it’s ready, perform the “windowpane test”: tear off a small piece of dough and gently stretch it between your fingers. If you can stretch it thin enough to see light through it without it tearing, it’s perfectly kneaded.
5. First Rise: Lightly grease a large, clean bowl with a little oil or cooking spray. Form your kneaded dough into a ball and place it in the bowl, turning it over once to coat the top with oil. Cover the bowl tightly with plastic wrap or a damp kitchen towel. Place it in a warm, draft-free spot to rise for 1 to 1.5 hours, or until it has doubled in size.

Part 2: Preparing the Filling and Assembling the Swirls

1. Make the Cream Cheese Filling: While the dough is rising, prepare the filling. In a medium bowl, combine the softened cream cheese and granulated sugar. Using an electric hand mixer or a sturdy whisk, beat until the mixture is completely smooth and creamy, with no lumps. Add the egg yolk, vanilla extract, and tablespoon of flour. Beat again until everything is well combined and the filling is glossy and smooth. Set it aside.
2. Roll Out the Dough: Once the dough has doubled in size, gently punch it down to release the air. Transfer the dough to a lightly floured work surface. Using a rolling pin, roll the dough out into a large rectangle, approximately 12 inches by 18 inches. The dough should be about ¼-inch thick.
3. Spread the Filling: Using an offset spatula or the back of a spoon, spread the prepared cream cheese filling evenly over the surface of the rolled-out dough. Be sure to leave about a ½-inch border clear along one of the long edges. This will help seal the log.
4. Roll and Slice: Starting from the long edge opposite the clear border, carefully and tightly roll the dough up into a log. A tight roll is crucial to prevent gaps in your swirls. Pinch the seam at the end to seal it firmly. Now, for the cutting: for the cleanest cuts, use a piece of unflavored dental floss or a very sharp serrated knife. Slide the floss under the log, bring the ends up, cross them over, and pull to slice through the dough. This prevents squishing the swirls. Cut the log into 12 equal 1.5-inch pieces.
5. Arrange for Second Rise: Grease a 9×13-inch baking pan or two 9-inch round cake pans. Place the sliced swirls cut-side up in the prepared pan(s), leaving a little space between each one as they will expand.
6. Second Rise: Cover the pan loosely with plastic wrap and let the swirls rise in a warm place for another 30-45 minutes, or until they look puffy and have filled in most of the gaps in the pan. While they rise, preheat your oven to 375°F (190°C).

Part 3: Baking and Glazing

1. Bake to Perfection: Once the second rise is complete, place the pan in the preheated oven. Bake for 20-25 minutes, or until the tops are a beautiful golden brown and the filling is set. The internal temperature of the dough should be around 190°F (88°C).
2. Cool Slightly: Remove the pan from the oven and place it on a wire rack to cool for about 10-15 minutes. It’s important to let them cool slightly before glazing so the glaze doesn’t melt and run right off.
3. Prepare and Apply the Glaze: While the swirls are cooling, whisk together the sifted powdered sugar, vanilla extract, and 2 tablespoons of milk in a small bowl. Add more milk, one teaspoon at a time, until you reach your desired drizzling consistency.
4. Drizzle and Serve: Drizzle the vanilla glaze generously over the warm sweet cream cheese swirls. Serve them warm for the ultimate decadent experience.