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

Add melted butter, egg, and salt, then gradually mix in all-purpose flour until a soft dough forms.

Knead the dough for about 5-7 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise for about 1 hour.

While the dough is rising, prepare peach filling by chopping peaches and mixing with brown sugar, cinnamon, and nutmeg.

Once dough has risen, punch it down and roll it out into a rectangle about 1/4-inch thick. Spread peach filling evenly over the dough.

Roll the dough tightly into a log and slice into 12 equal rolls. Place them cut-side up in a greased baking pan.

Cover rolls lightly with a kitchen towel and let them rise for another 30-40 minutes.

Preheat oven to 350°F (175°C). Bake the rolls for 25-30 minutes until golden brown.

For the glaze, whisk together powdered sugar, milk, and vanilla extract until smooth and drizzle over warm rolls.