Cook the shallots in butter until translucent, about 5 minutes Add remaining ingredients and bring to a boil, then drop to a simmer and cook until fruit is very tender, about 15 minutes. Puree mixture and pass through a fine mesh strainer to remove fine seeds. Taste to adjust seasoning and tartness, and then chill to hold.
Assembly: Cook oatmeal in water and orange juice Stir in one tablespoon of berry gastrique mixture. Serve each portion of oatmeal with a garnish of fresh fruit, walnuts, basil, and a drizzle of the berry gastrique.