In a small bowl, combine the lukewarm milk and active dry yeast, stirring gently. Allow the mixture to sit for 5-10 minutes until it becomes frothy, indicating the yeast is active and ready.

In a large mixing bowl, combine the all-purpose flour, granulated sugar, and salt. Next, add the activated yeast mixture, softened butter, egg, and vanilla extract. Mix until a cohesive dough forms.

Transfer the dough to a lightly floured surface and knead for about 8-10 minutes until it becomes smooth and elastic.

Place the kneaded dough into a greased bowl. Cover it with a clean kitchen towel and set it in a warm spot for 1 to 1.5 hours, or until doubled in size.

In a medium bowl, beat the cream cheese until smooth and creamy. Gradually mix in sugar, vanilla extract, flour, and sour cream until fully incorporated.

In a separate bowl, combine the brown sugar, ground cinnamon, and salt.

After the first rise, punch down the dough to release air. Roll it out on a lightly floured surface into a rectangle measuring about 16x12 inches. Spread a thin layer of softened butter, then distribute the cheesecake filling and cinnamon sugar mixture.

Starting from one long edge, roll the dough tightly into a log. Pinch the seam to seal and slice the log into 12 equal pieces. Place these cut rolls in a greased baking dish.

Cover the rolls with a kitchen towel and let them rise in a warm environment for another 30-45 minutes.

Preheat your oven to 350°F (175°C). Once preheated, bake the rolls for 25-30 minutes, or until golden brown.

While the rolls are baking, prepare the icing by beating together the cream cheese, powdered sugar, vanilla extract, and enough milk to achieve a smooth consistency.

Once the rolls are baked, let them cool slightly before drizzling the icing over the top. Add sliced strawberries and serve warm.