Bring the stock to a boil in a 6-qt. saucepan. Reduce heat to medium-low and add okra, bay leaves, and onions. Cook, stirring occasionally, until okra is very tender and stock has reduced by one-quarter, about 1½ hours.
Stir palm oil, 3 tbsp. fish sauce, the chiles, and eggplant into the broth. Cook, stirring occasionally, until stew is thickened and okra falls