Warm milk to 110°F, then stir in yeast and 1 tablespoon sugar. Let sit 5–10 minutes until foamy.
Add remaining sugar, melted butter, egg, yolk, and salt to yeast mixture. Mix in flour gradually, then knead 6–8 minutes until smooth and elastic.
Shape dough into a ball, place in greased bowl, cover, and let rise in warm spot for about 1 hour until doubled.
Peel and dice peaches, toss with cornstarch. In a separate bowl, mix brown sugar, cinnamon, nutmeg, and salt.
Punch down dough and roll into a 12x18-inch rectangle on a floured surface.
Spread softened butter over dough, leaving a 1-inch border. Sprinkle with sugar mixture, then scatter peaches on top. Roll tightly into a log and pinch seam closed.
Trim uneven ends and slice log into 12 even rolls using floss or a serrated knife.
Place rolls cut side up in greased 9x13-inch dish, cover, and let rise 30–45 minutes until puffy and touching.
Preheat oven to 350°F. Bake rolls 22–25 minutes until golden brown. Tent with foil if browning too quickly.
While rolls bake, beat cream cheese and butter until smooth. Add powdered sugar and vanilla, then thin with milk to drizzling consistency. Spread over warm rolls.