This recipe has been adapted from "Craft of Cooking" by Tom Colicchio.
In a large straight-sided skillet, heat olive oil over medium heat. Add onion, carrot, and celery. Season with salt and pepper. Cook, stirring occasionally until vegetables are tender, about 20 minutes. Add bay leaf, thyme, and endives. Stir to coat with oil. Add vinegar, wine, verjus, and enough water to cover. Season again with salt and pepper.
Cover with parchment paper and then the lid. Simmer over medium-low heat until endives are tender when pierced with the tip of a knife, about 50 minutes. Discard bay leaf. Halve endive lengthwise, and serve with some of the braising liquid.