Combine the warm milk, active dry yeast, and a small pinch of the measured granulated sugar. Allow the mixture to stand for approximately 5 minutes, or until the surface appears foamy and active.
Place the remaining granulated sugar, melted butter, salt, eggs, and all-purpose flour in a large mixing bowl. Add the activated yeast mixture and stir until a cohesive dough develops.
Transfer the dough to a lightly floured work surface. Knead for 8 to 10 minutes, continuing until the dough becomes smooth and elastic. Place it in a lightly greased bowl, cover, and leave it in a warm location for about 1 hour, or until doubled in volume.
In a medium bowl, mix the diced peaches with the packed brown sugar and ground cinnamon. Stir thoroughly so the fruit is evenly coated, then set the filling aside while the dough completes its first rise.
Gently deflate the risen dough and place it on a floured surface. Roll it into a large rectangle measuring approximately ¼ inch in thickness.
Distribute the peach mixture evenly across the rolled dough. Beginning at one long edge, carefully roll the dough into a firm log.
Cut the log into 12 equal portions and arrange them in a greased baking dish. Cover the dish and allow the rolls to rise for another 30 minutes, or until visibly puffed.
Preheat the oven to 350°F (175°C). Bake the fully proofed rolls for approximately 25 minutes, until golden on top and completely baked through. Let them cool briefly before applying the frosting.
Beat the softened cream cheese and butter together until creamy and uniform. Add the confectioners’ sugar and vanilla extract, then continue beating until the frosting is light, smooth, and easy to spread.
Spread or drizzle the cream cheese frosting over the rolls while they are still warm for a softer, partially melted coating. For a thicker finish, allow the rolls to cool slightly longer before frosting. Serve warm.