Making the Dough

1. In the bowl of a stand mixer, combine the warm milk, sugar, and yeast. Whisk lightly and let it sit for about 10 minutes until the yeast becomes foamy. This step is crucial for activating the yeast and ensuring a good rise.
2. Add the softened butter, eggs, egg yolk, flour, and salt. Use a dough hook attachment and mix on medium speed until a soft dough forms. This should take about 6-8 minutes. The dough should be smooth and slightly tacky but should pull away from the sides of the bowl.
3. Grease a clean bowl with cooking spray or a small amount of oil. Transfer the dough into the bowl, cover it with a clean kitchen towel, and let it rise for about an hour or until doubled in size.

Preparing the Strawberry Filling

1. In a medium saucepan, combine the chopped strawberries, sugar, and lemon juice. Cook over medium heat, stirring frequently, until the fruit starts to break down and become syrupy.
2. In a small bowl, mix the cornstarch with two tablespoons of water until smooth. Add this mixture to the saucepan along with the cinnamon.
3. Bring the mixture to a low boil, then reduce the heat and simmer for about five minutes, stirring occasionally, until the filling becomes thick and glossy.
4. Remove from heat and let it cool completely before using. Reserve two tablespoons of the filling for the icing.

Shaping the Dough

1. Once the dough has risen, gently punch it down to release excess air. Transfer it to a lightly floured surface and roll it into a 15×10-inch rectangle.
2. Evenly spread the cooled strawberry filling over the surface of the dough, leaving a small border around the edges.
3. Starting from one long edge, roll the dough tightly into a log. Using a sharp knife or unflavored dental floss, cut the log into 12 equal pieces.
4. Grease a 9×13-inch baking pan with butter and arrange the rolls inside, leaving space between them for rising. Cover the pan and let the rolls rise again for about 45 minutes or until doubled in size.

Baking the Rolls

1. Preheat the oven to 375°F.
2. Lightly brush the tops of the rolls with cream to enhance browning and provide a soft crust.
3. Bake for 20-25 minutes or until the rolls are golden brown and have an internal temperature of 190°F. If they brown too quickly, loosely tent them with foil during the last 10 minutes of baking.
4. Remove from the oven and allow the rolls to cool slightly on a wire rack.

Making the Icing

1. In a mixing bowl, beat the softened cream cheese and butter until smooth and creamy.
2. Gradually add the powdered sugar, beating continuously to avoid lumps.
3. Mix in the reserved strawberry filling and add milk as needed until the desired consistency is reached. The icing should be thick yet spreadable.
4. Once the rolls have cooled slightly but are still warm, spread the icing generously over the tops.