Warm the milk and mix it with sugar and yeast until foamy. Add the eggs, softened butter, salt, and flour, then knead until the dough is smooth and elastic. Let it rise until doubled in size.
Cook the diced peaches with brown sugar, cinnamon, cornstarch, and vanilla until thick and glossy. Let the filling cool so it spreads easily without making the dough too soft.
Roll the dough into a rectangle and spread a layer of softened butter over the surface. Add the peach filling evenly, then sprinkle with a little extra cinnamon sugar if you want more sweetness.
Roll the dough up tightly from the long side, then cut into even pieces. Arrange them in a greased baking dish with a little space between each roll.
Let the rolls rise again until puffy, then bake until golden brown and cooked through. The edges should be lightly caramelized and the centers soft.
Beat the cream cheese, powdered sugar, and a splash of milk or cream until smooth. Spread the glaze over the warm rolls so it melts into the swirls.