In a heavy saucepan, warm oil over medium heat. Sauté onions and celery until very tender, about 20 minutes. Stir in sugar, cider vinegar, salt, pepper, turmeric, pimentos and 2 Tbsp. water. Reduce heat to low and simmer, uncovered, stirring occasionally, until liquid has almost evaporated, about 25 minutes. Transfer to a bowl and cool completely.