Mix warm milk, a teaspoon of sugar, and the yeast in a bowl and let sit until foamy, about 5 minutes.
In a large bowl, combine flour, remaining sugar, salt, and melted butter. Add the proofed yeast mixture and knead until a soft, slightly sticky dough forms, about 5 minutes.
Cover the dough with a clean towel and let it rise in a warm spot until doubled in size, about 1 hour.
While the dough rises, beat the softened cream cheese with powdered sugar and vanilla until smooth and creamy. Gently fold in sliced strawberries.
Preheat the oven to 375°F (190°C). Punch down the risen dough and roll it out on a floured surface into a rectangle about ¼ inch thick.
Spread the cream cheese and strawberry filling evenly over the rolled-out dough, leaving a small border around the edges.
Carefully roll the dough tightly into a log, starting from one long edge, to encase the filling.
Cut the rolled log into 8 equal slices and arrange them cut-side up in a greased baking dish or on a baking sheet.
Brush the tops with beaten egg for a shiny, golden finish. Bake in the preheated oven for 20 minutes, or until the edges are golden brown and the centers are bubbling.
Remove from the oven and let cool slightly. Serve warm to enjoy the crunchy edges and creamy, fruity filling.
