Make the peach filling: Combine diced peaches, brown sugar, cornstarch, lemon juice, and vanilla in a saucepan over medium heat. Cook for 8-10 minutes until thickened. Cool completely.
Activate yeast: Warm milk to 110°F, stir in yeast with 1 tablespoon sugar. Let sit 5 minutes until foamy.
Make dough: In stand mixer, combine yeast mixture, remaining sugar, eggs, and melted butter. Add flour and salt. Knead 7-8 minutes until smooth.
First rise: Place dough in greased bowl, cover, and rise 1 hour until doubled.
Make crumb topping: Mix flour, oats, brown sugar, and cold butter until crumbly. Refrigerate.
Assemble rolls: Roll dough into 12x18 inch rectangle. Spread with softened butter, then brown sugar and cinnamon. Top with cooled peach filling.
Roll and cut: Roll tightly from long side, pinch seam. Cut into 12 equal rolls.
Second rise: Arrange in greased 9x13 dish, cover, rise 30-40 minutes until puffy.
Bake: Preheat oven to 350°F. Sprinkle crumb topping over rolls. Bake 25-30 minutes until golden.
Make glaze: Whisk powdered sugar, cream, vanilla, and salt until smooth. Drizzle over warm rolls.