01 - Combine warm milk, warm water, sugar, and yeast in a large bowl. Let stand 5–10 minutes until mixture becomes foamy and fragrant.
02 - Stir melted butter, eggs, and salt into the yeast mixture. Gradually add flour, mixing until a soft, shaggy dough forms.
03 - Turn dough onto a lightly floured surface and knead for 8–10 minutes until smooth, elastic, and no longer sticky. Place in a greased bowl, cover, and let rise in a warm area for 1–1.5 hours until doubled in volume.
04 - Melt butter in a saucepan over medium heat. Add peaches, brown sugar, cornstarch, cinnamon, and nutmeg. Cook, stirring constantly, for 5–7 minutes until peaches are tender and sauce has thickened. Transfer to a bowl and cool completely.
05 - In a small bowl, combine brown sugar and cinnamon until evenly blended. Set aside.
06 - Punch down risen dough and roll out on a floured surface into a 16x12-inch rectangle. Spread softened butter evenly over surface. Sprinkle with cinnamon sugar mixture, then distribute cooled peach filling across the dough.
07 - Starting from a long side, roll dough tightly into a log. Slice into 12 equal pieces and arrange in a greased 9x13-inch baking dish. Cover and let rise for 30–45 minutes until puffy.
08 - Bake at 350°F for 25–30 minutes until rolls are golden brown and cooked through. Allow to cool in pan for 10 minutes.
09 - Whisk powdered sugar, milk, vanilla extract, and salt in a small bowl until smooth and pourable.
10 - Drizzle vanilla glaze generously over warm rolls. Serve immediately while still slightly warm.