01 - Pour warm milk into a large mixing bowl and sprinkle the active dry yeast over the surface. Let the mixture stand for 5 minutes until it becomes frothy and bubbly, indicating the yeast is active.
02 - Add the melted butter, egg, granulated sugar, and salt to the yeast mixture. Gradually incorporate the all-purpose flour, stirring until a shaggy dough begins to form. Turn the dough onto a lightly floured surface and knead for 5 to 8 minutes until it becomes smooth, elastic, and slightly tacky to the touch.
03 - Shape the dough into a ball and place it in a lightly oiled bowl, turning once to coat all sides. Cover tightly with plastic wrap or a clean kitchen towel and set in a warm, draft-free spot. Allow the dough to rise until doubled in size, approximately 1 hour.
04 - While the dough rises, combine the softened cream cheese, granulated sugar, and vanilla extract in a medium bowl. Beat with a hand mixer or whisk until the mixture is completely smooth and creamy with no lumps remaining.
05 - In a separate bowl, toss the diced fresh strawberries with the granulated sugar and cornstarch until the strawberries are evenly coated. The cornstarch will help thicken the juices during baking.
06 - Punch down the risen dough to release air bubbles. On a lightly floured surface, roll the dough into a 12×16-inch rectangle. Spread the cheesecake filling evenly across the surface, leaving a 1/2-inch border along all edges. Sprinkle the strawberry mixture in an even layer over the cream cheese filling.
07 - Starting from one long side, gently but tightly roll the dough into a log, keeping the filling centered. Pinch the seam firmly to seal. Using a sharp knife, cut the log into 12 equal-sized rolls.
08 - Arrange the rolls cut-side up in a greased 9×13-inch baking pan. Cover loosely with a towel and let them rise for 20 to 30 minutes until slightly puffy and expanded.
09 - Preheat the oven to 350°F. Bake the rolls for 22 to 25 minutes until the tops are golden brown and the centers appear set. Remove from the oven and allow to cool in the pan for 10 minutes.
10 - Whisk together the powdered sugar, 2 tablespoons of milk, and vanilla extract until a smooth, pourable glaze forms. Add the remaining tablespoon of milk if a thinner consistency is desired. Drizzle the glaze over the slightly cooled rolls and serve warm.