In a saucepan, heat oil over medium-low. Add shallots and ginger and cook, stirring occasionally, until shallots are translucent, about 3 minutes.
Add rhubarb and red tart cherries along with liquid from both cans. Stir in brown sugar bring to a boil; reduce heat to a gentle simmer. Cook until fruit has softened and mixture is thick, adjusting heat as necessary to prevent scorching, 25-30 minutes. Stir occasionally, being careful not to break up the fruit. Stir in vinegar and orange zest; season with salt and pepper and let cool completely before using.