Melt half a stick of unsalted butter and combine it with warmed milk in a mixing bowl (100-110°F) to activate the yeast. Add granulated sugar, yeast, salt, and a beaten egg to the mixture. Gradually stir in sifted all-purpose flour until a soft, slightly sticky dough forms. Knead on a floured surface for about 5 minutes, then place it in a greased bowl and let it proof in a warm oven for 10 minutes until it has risen slightly.

While the dough rises, create the filling by mixing softened butter, light brown sugar, and ground cinnamon in a small bowl. Use a fork or spatula to blend until the mixture is smooth and creamy.

Once the dough has risen, turn it out onto a floured surface and roll it into a rectangle, about 1/4 inch thick. Evenly spread the prepared filling across the dough, leaving a small border around the edges. Roll the dough tightly from one long side to the other, forming a log. Using a serrated knife or unflavored dental floss, cut the roll into even slices, approximately 1-2 inches in width.

Grease a baking pan and arrange the cinnamon roll slices inside, ensuring they are snug but not overcrowded. Preheat your oven to 350°F and bake the rolls for 20-25 minutes.

Once removed from the oven, let the cinnamon rolls cool in the pan for about 10 minutes. Meanwhile, prepare your cream cheese icing by whipping together softened cream cheese, powdered sugar, and vanilla extract. Spread the icing generously over the warm rolls.