Make the dough: In the bowl of a stand mixer, combine the 3/4 cup warm milk, 1/4 cup sugar, and 2 1/4 teaspoons yeast. Whisk and then set aside to bloom for about 10 minutes until foamy.
Add the 1/3 cup softened butter, 2 eggs + 1 yolk, 3 1/4 cups bread flour, and 1/2 teaspoon salt to the bowl. Beat with a dough hook on medium until a soft dough forms, about 6-8 minutes. It should be smooth and pull away from the sides of the bowl.
Grease a clean bowl with cooking spray or vegetable oil. Transfer the dough to the bowl, cover it with a clean kitchen towel, and let it proof/rise for about an hour or until doubled in size.
Make the filling: Meanwhile, combine the 2 cups chopped strawberries, 1/2 cup sugar, and 1 teaspoon lemon juice in a saucepan and cook over medium heat, stirring frequently, until the fruit is slightly broken down and thick.
Mix the 1 tablespoon cornstarch with 2 tablespoons of water until smooth, then add to the pot along with the 1/2 teaspoon cinnamon. Bring to a low boil, reduce the heat to low, and simmer until thick and shiny, about 5 minutes. Remove from heat and let cool completely. Reserve 2 tablespoons of the filling for the icing.
Form the dough: When the dough has doubled in size, punch the air out and turn it onto a lightly floured surface. Roll it into a 15×10-inch rectangle and spread the cooled strawberry filling over the surface, not quite to the edges.
Tightly roll the dough into a log, then cut into 12 equally-sized rolls (dental floss works great for this!). Grease a 9×13-inch baking pan with butter and arrange the rolls inside. Cover again and let proof/rise until doubled in size, about 45 minutes.
Bake the rolls: Preheat the oven to 375°F. Brush the rolls with cream (optional) and bake for 20-25 minutes or until the internal temperature reaches 190°F. Remove from the oven and cool completely on a wire rack.
Make the icing: In a large bowl, beat the 4 ounces cream cheese and 2 tablespoons butter until smooth. Gradually add the 1 cup powdered sugar and reserved strawberry filling, then mix in milk as needed until the desired consistency is reached.
When the rolls are cool (or slightly warm), spread the glaze over the top. Serve and enjoy! 🍴💖