Preheat your oven to 375°F (190°C) and grease a 9x13-inch baking dish.
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt.
In a separate bowl, combine the melted butter, milk, egg, and vanilla extract. Pour the wet ingredients into the dry ingredients and mix until just combined.
On a floured surface, roll out the dough into a rectangle about 1/4 inch thick.
In a small bowl, mix together the diced peaches, brown sugar, cinnamon, cornstarch, and lemon juice. Spread this mixture evenly over the rolled-out dough.
Starting from one long edge, carefully roll the dough into a tight log. Slice the log into 12 equal pieces.
Place the rolls in the prepared baking dish and bake for 25-30 minutes or until golden brown.
While the rolls are baking, prepare the topping by whisking together the powdered sugar, milk, and vanilla extract until smooth.
Once the rolls are done baking, drizzle the topping over the warm rolls and let cool slightly before serving.