In a small saucepan, mix the milk, warm water, yeast, and granulated sugar. Heat until warm but not boiling. Remove from heat and let it sit for a minute to activate the yeast.

Combine the flour, salt, and sugar in a large mixing bowl. Mix well. Add the egg and pour in the warm milk and yeast mixture. Stir until a soft dough forms.

Transfer the dough onto a lightly floured surface. Knead for about 5 minutes, until the dough becomes smooth and elastic.

Place the dough in a greased bowl and cover with plastic wrap or a clean kitchen towel. Allow it to rise in a warm place for about 1 hour, or until it doubles in size.

While the dough is rising, make the filling. Mix the melted butter, brown sugar, and ground cinnamon in a small bowl until well combined.

Once the dough has risen, punch it down to release any air bubbles. Roll it out into a rectangle shape, about ¼ inch thick.

Spread the filling evenly over the dough, leaving a small border around the edges.

Starting from one of the longer sides, tightly roll the dough into a log shape. Pinch the seam to seal.

Cut the log into 9 equal-sized pieces using a sharp knife.

Place the cinnamon rolls in a greased 8×8-inch baking dish, leaving a little space between each roll. Cover with a kitchen towel and let them rise for another 30 minutes.

Preheat the oven to 375°F.

Bake the cinnamon rolls for 15-20 minutes, or until golden brown.

While the cinnamon rolls are baking, prepare the glaze. In a small bowl, whisk together the powdered sugar, softened cream cheese, and vanilla extract until smooth.

Once the cinnamon rolls are done baking, remove them from the oven and let them cool for a few minutes.

Drizzle the glaze over the warm cinnamon rolls.