Make the dough base
In a large bowl, whisk together flour, sugar, salt, and yeast. Set aside.

Warm liquids and butter
In a small saucepan (or microwave-safe cup), heat water, milk, and butter until the butter melts and the mixture is warm—not hot—to the touch (about 110°F).

Combine wet and dry
Pour the warm mixture into the dry ingredients. Add the egg and stir until a soft dough forms.

Knead the dough
Transfer the dough to a floured surface and knead for 3–5 minutes until smooth and elastic. Add more flour if needed.

First rise
Place the dough in a greased bowl, cover with a towel, and let it rise in a warm spot for 1 to 1.5 hours or until doubled in size.

Prepare the filling
Mix softened butter, cinnamon, and brown sugar into a paste.

Roll and fill
Roll the dough into a 14×8-inch rectangle. Spread the cinnamon mixture evenly over the surface.

Form rolls
Roll the dough tightly into a log starting from the long edge. Slice into 9–12 rolls and place them in a greased 9-inch pan.

Second rise
Cover and let the rolls rise for 30–45 minutes until puffy.

Bake
Preheat oven to 375°F (190°C). Bake rolls for 20–25 minutes or until golden brown.

Make the glaze
Whisk powdered sugar, vanilla, and milk or coffee until smooth.

Glaze and serve
Drizzle glaze over warm rolls. Serve immediately for gooey perfection.