In a mixing bowl, combine warm milk, sugar, and yeast. Let it sit for about 5 minutes until frothy.
Add flour (3-½ cups), egg, butter, vanilla, and salt to the yeast mixture. Mix until a dough forms, then knead in the remaining ¼ cup flour until smooth.
Roll the dough out into a rectangle. Spread the strawberry jam, chopped strawberries, and cinnamon over the dough.
Roll the dough tightly and cut into 12 rolls. Place on a baking sheet and let rise for 30 minutes.
Bake at 350°F (175°C) for 25 minutes or until golden brown.
For the glaze, beat together cream cheese, butter, confectioners' sugar, milk, and vanilla until smooth. Drizzle over warm rolls before serving.
Notes
These rolls are best served warm. You can add more fruits or nuts for extra flavor.