In a small bowl, dissolve the cornstarch in the water.
In a medium saucepan, combine the peaches with the granulated sugar, brown sugar, salt and orange juice and bring to a simmer over moderate heat, stirring until the sugar dissolves. Cook for 5 minutes,stirring occasionally. Add the ginger and cinnamon and simmer for 2 minutes longer. Add the dissolved cornstarch and simmer until the liquid is slightly thickened, about 30 seconds.
Using an immersion blender, gently pulse until a chunky sauce forms. Serve chilled.