Preheat oven to 350°F and grease a 9-inch square baking pan.
Make the peach filling: Melt 2 tablespoons butter in a medium saucepan over medium heat. Add diced peaches, 1/4 cup brown sugar, 2 tablespoons granulated sugar, cornstarch, 1 teaspoon cinnamon, vanilla, 1/4 teaspoon salt, and lemon juice. Cook for 5-7 minutes, stirring occasionally, until peaches soften and mixture thickens. Set aside to cool slightly.
Make the crumble topping: In a small bowl, combine flour, oats, 2 tablespoons brown sugar, 1/4 teaspoon cinnamon, and pinch of salt. Work in 3 tablespoons cold cubed butter with your fingers until mixture resembles coarse crumbs.
Separate the cinnamon rolls and cut each into quarters. Arrange in prepared baking pan with space between pieces.
Spoon the peach filling over and around the cinnamon roll pieces. Sprinkle crumble topping evenly over everything.
Bake for 25-30 minutes until golden brown, filling is bubbling, and a toothpick inserted in center comes out clean. Cool for 10 minutes, then drizzle with included icing. Serve warm.