In a mixing bowl, combine warm milk, sugar, and yeast. Let it sit for 5 minutes until frothy.

Add melted butter, egg, and salt to the yeast mixture. Gradually mix in flour until a dough forms.

Knead the dough on a floured surface for about 5 minutes until smooth. Place in a greased bowl, cover, and let rise for 1 hour.

In a separate bowl, mix chopped peaches, brown sugar, cinnamon, and softened butter until well combined.

Preheat the oven to 350°F (175°C). Roll out the dough into a rectangle on a floured surface.

Spread the peach filling evenly over the dough. Roll the dough tightly into a log and slice into 8 rolls.

Place the rolls in a greased baking dish and let them rise for another 30 minutes.

Bake the rolls in the preheated oven for 20-25 minutes until golden brown.

While baking, whisk together powdered sugar, milk, and vanilla extract to make the glaze.

Drizzle the glaze over the warm rolls before serving.