In a bowl, combine warm milk and sugar. Sprinkle yeast over the mixture and let it sit for 5-10 minutes until it becomes frothy.
In a large bowl, mix the activated yeast mixture, melted butter, egg, salt, and flour. Knead the dough until it's smooth and elastic. Cover the bowl and let the dough rise in a warm place for about an hour until it doubles in size.
Mix the softened butter, brown sugar, and ground cinnamon in a small bowl until it forms a smooth paste.
Once the dough has risen, punch it down and roll it out into a rectangle on a floured surface. Spread the filling mixture evenly over the dough.
Carefully roll the dough into a log, starting from one of the longer sides. Seal the seam by pinching the edges together.
Using a sharp knife or dental floss, cut the log into 1-inch thick slices. You should get around 8-10 rolls.
Preheat your air fryer to 320°F (160°C).
Place the cinnamon rolls in the air fryer basket, leaving some space between them to allow for expansion.
Cook the cinnamon rolls in the air fryer for about 10-12 minutes, or until they turn golden brown and are cooked through. Cooking time may vary depending on the air fryer model.
While the rolls are cooking, mix powdered sugar, milk, and vanilla extract (if using) to make the glaze. Adjust the consistency by adding more milk if needed.
Once the cinnamon rolls are done, drizzle them with the prepared glaze while they're still warm. Serve and enjoy!