In a stand mixer bowl, combine the flour, instant yeast, and sugar. Add the warm milk (110°F), softened butter, egg, and salt. Use the dough hook on low speed until a shaggy dough forms.
Increase the speed to medium and knead for 5–7 minutes. The dough should be smooth, elastic, and pull away from the sides of the bowl.
Cover and let rise in a warm spot for 1–1.5 hours, or until doubled in size.
Punch down the dough and roll it out into a 12x18-inch rectangle on a floured surface.
Spread the cooled strawberry filling evenly, leaving a small border at the edges.
Evenly sprinkle brown sugar and cinnamon over the strawberry layer. This creates a rich, caramelized flavor that pairs perfectly with the fresh fruit.
Roll the dough tightly into a log. Cut into 12 even rolls using a sharp knife or unflavored dental floss. Place in a greased 9x13 pan. Cover and let rise for 30–45 minutes until puffy.
Bake at 350°F (175°C) for 22–27 minutes until the edges are lightly golden.
Beat the softened full-fat cream cheese and butter until smooth and pale (about 2 minutes).
Gradually add sifted powdered sugar on low speed until fully incorporated. Mix in the vanilla and 1 tablespoon of strawberry reduction until the frosting is a uniform pink.
Spread over the rolls 5–10 minutes after they come out of the oven. This allows the frosting to seep into the centers while remaining thick on top.