01 - In a small bowl, combine warm milk (110°F), active dry yeast, and 1 tablespoon of sugar. Stir gently and let stand for 5 to 10 minutes until the mixture becomes frothy and bubbly, indicating the yeast is active.
02 - In a large mixing bowl, whisk together the eggs, melted butter, remaining sugar, and salt until well combined. Pour in the activated yeast mixture and stir to incorporate.
03 - Gradually add the flour, mixing until a soft, slightly tacky dough forms. Turn out onto a lightly floured surface and knead by hand for 5 to 7 minutes until the dough is smooth, elastic, and springs back when pressed.
04 - Transfer the dough to a lightly greased bowl, turning once to coat. Cover with a clean kitchen towel or plastic wrap and set in a warm, draft-free spot until doubled in size, approximately 1 hour.
05 - While the dough rises, combine the chopped strawberries, sugar, and cornstarch in a small saucepan over medium heat. Cook, stirring constantly, for 3 to 5 minutes until the mixture thickens to a jammy consistency. Remove from heat and let cool completely.
06 - Using an electric mixer, beat the softened cream cheese, sugar, and vanilla extract on medium speed until perfectly smooth and creamy, scraping the bowl as needed.
07 - Punch down the risen dough and turn it out onto a floured surface. Roll into a 16x10-inch rectangle. Spread the cream cheese filling evenly over the dough, then gently layer the cooled strawberry mixture on top.
08 - Starting from the long edge, roll the dough up tightly into a log. Using a sharp knife or dental floss, cut into 12 equal pieces. Place the rolls cut-side down in a greased 9x13-inch baking dish.
09 - Cover the dish and let the rolls rise in a warm place for 30 minutes until puffy and nearly doubled.
10 - Preheat the oven to 350°F. Bake the rolls for 22 to 25 minutes until the tops are lightly golden and the centers are cooked through. Remove from the oven and let cool slightly.
11 - Whisk together the powdered sugar, milk, and vanilla extract until smooth and pourable. Drizzle generously over the warm rolls and serve immediately.