1. Make the Dough: In a large bowl, whisk together flour, granulated sugar, yeast, and salt.
2. In a separate bowl, whisk together warm milk, softened butter, and egg until combined.
3. Pour the wet ingredients into the dry ingredients and mix until a shaggy dough forms.
4. Turn the dough out onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook.
5. Place the dough in a greased bowl, cover with plastic wrap, and let it rise in a warm place for 1-1.5 hours, or until doubled in size.
6. Prepare the Filling: In a small bowl, mix together brown sugar and cinnamon. Set aside.
7. Make the Glaze: In a medium bowl, beat softened cream cheese and softened butter until smooth. Gradually add powdered sugar and vanilla extract, beating until combined. Add milk 1 tablespoon at a time until desired glaze consistency is reached.
8. Assemble the Rolls: Punch down the risen dough and turn it out onto a lightly floured surface. Roll it into a large rectangle, approximately 12×18 inches.
9. Spread the 1/4 cup of softened butter evenly over the dough, leaving a small border on one long edge.
10. Sprinkle the cinnamon-sugar mixture evenly over the buttered dough.
11. Starting from the long edge with the filling, tightly roll up the dough into a log. Pinch the seam to seal.
12. Cut the log into 12 equal slices (about 1.5 inches thick).
13. Place the cinnamon rolls cut-side up in a greased 9×13 inch baking dish.
14. Let the rolls rise again, uncovered, for 30-45 minutes, or until puffy.
15. Preheat oven to 375°F (190°C).
16. Bake for 20-25 minutes, or until golden brown and cooked through.
17. Let the rolls cool slightly in the pan for about 5-10 minutes before drizzling generously with the creamy glaze.