In the bowl of a stand mixer fitted with a dough hook, stir together the warm milk and sugar. Sprinkle the yeast on top and let it sit until foamy, 5 to 10 minutes. Editor's Tip: This step is key whenever you're using yeast—that is, active dry yeast. Activating it ensures it's ready to get to work. If the mixture does not get foamy after 10 minutes, discard it and start over with a new packet of yeast.

Turn the mixer speed to medium and gradually mix in 3-½ cups flour, the egg, butter, vanilla extract and salt. Mix until the dough comes together and pulls away from the sides. Transfer the dough to a greased bowl. Cover the bowl with a towel and let the dough rise at room temperature for 1 hour 30 minutes to 2 hours or until the dough has doubled in size.

Sprinkle a cutting board with the remaining ¼ cup flour. Transfer the dough to the floured surface. Use a rolling pin to roll the dough into a ¼-inch-thick rectangle.

Use a knife to cut eight evenly sized strips of dough down the length of the rectangle. In a small bowl, stir together the strawberry jam, chopped strawberries and cinnamon. Using a spatula, spread the mixture evenly over the dough. Starting with the long end of each strip, tightly roll up the dough to form a roll. Repeat with all eight strips. Place the rolls in a greased 13x9-inch baking dish. Cover the baking dish with a towel and let the rolls rise for an additional 30 minutes. Preheat the oven to 350°. Editor's Tip: Strawberry jam is a messy filling, so it's easier to cut strips of dough and roll them individually. However, you can still choose to use the traditional method of spreading the filling over the dough, rolling it into a log and slicing the log with a sharp knife if you prefer.

Bake the rolls for 35 to 38 minutes or until the edges are lightly golden brown.

While the rolls are baking, place the softened cream cheese and butter in a large mixing bowl. Beat on medium speed until smooth, two to three minutes. Gradually mix in the confectioners' sugar, milk and vanilla extract, and beat for another one to two minutes. Spread the cream cheese glaze over the warm cinnamon rolls and serve immediately.