Mix warm milk, sugar, and yeast in a bowl. Let sit for 5 minutes until frothy.
Add melted butter, egg, and flour. Knead until a smooth dough forms, about 7 minutes.
Rise the dough in a greased bowl for 1 hour until doubled in size.
Roll dough into a 12x15 inch rectangle. Top with diced strawberries mixed with cornstarch.
Roll tightly into a log and cut into 12 slices. Place in a greased baking dish and let rise for 30 minutes.
Bake at 350°F for 20-25 minutes. Whisk icing ingredients and drizzle over warm rolls.