In the bowl of a stand mixer, combine 1 cup warm milk, 1 tablespoon instant dry yeast, 2 tablespoons granulated sugar, 1 teaspoon salt, 3 tablespoons salted butter and 1 large egg. Add in 3 cups all-purpose flour. Use a dough hook and turn on to a low speed.
Once the flour starts to incorporate into the dough, increase the speed to a medium range. Add additional flour as necessary so that the dough pulls away from the sides of the bowl. The dough mixture should be soft and tacky, but not stick to your hands. The amount of flour you add in bread making is always an approximation and you should go by feel.
Transfer the dough to a lightly greased mixing bowl. Cover with a towel and let rise until double in size, about 1 hour.
Filling and Baking
Lightly grease a baking sheet or 9x13 pan. Punch down the dough and roll into a 12 by 18-inch rectangle.
Spread 4 ounces cream cheese (softened) across the dough up to 1 inch away from the edge. Then spread 1/2 cup Strawberry jam on top of the cream cheese. Sprinkle 2 tablespoons brown sugar across the strawberry jam layer.
Roll up tightly lengthwise so you have one long roll. Use a sharp knife to gently cut the dough into 12 one-inch slices.
Place the slices onto a lightly 9x13 pan. Cover and let rise 30 to 45 minutes.
Preheat oven to 325 degrees Fahrenheit. Bake the rolls for about 18 minutes, until just kissed with brown on top.
Cream Cheese Frosting
While the rolls are baking, make the cream cheese frosting by using a hand mixer to whip together 4 ounces cream cheese and 1/4 cup salted butter in a bowl until light and fluffy. Whip in the powdered sugar 1/2 cup at a time until the desired consistency is reached. Add 1-2 tablespoons milk to thin it out as necessary.
Spread the cream cheese frosting across the rolls when they have cooled down just a bit, but are still warm.
Notes
For additional strawberry flavor, add 1/4 cup of strawberry preserves to the frosting.
No stand mixer? No problem! Start by stirring the ingredients together with a wooden spoon or spatula until the mixture becomes too thick to stir. Then place the dough on a clean, lightly floured surface and knead it for about 8-10 minutes, adding more flour as necessary, until the dough is soft, smooth, and tacky to the touch.