How to Make It
Preheat the oven to 400º. In a large ovenproof skillet, melt 1 tablespoon of the butter in 1 tablespoon of the olive oil. Season the pork roast all over with salt and pepper. Add the pork, thyme sprigs and garlic cloves to the skillet. Cook over moderate heat, turning occasionally, until the pork is browned on all sides, about 10 minutes. Transfer the skillet to the oven and roast the pork for about 1 hour, turning the meat and basting it with the pan juices every 15 minutes, until an instant-read thermometer inserted in the thickest part of the meat registers 165º. Transfer the pork to a rack set over a baking sheet and let rest for 30 minutes.
Meanwhile, in a large saucepan, melt 2 tablespoons of the butter in 1 tablespoon of the olive oil. Add the onions and cook over moderately low heat, stirring occasionally, until they are very soft but not browned, about 30 minutes. Add the buttermilk, bring to a simmer and cook, stirring occasionally, until the liquid is reduced and the onions are very tender, about 20 minutes. Transfer the onion-buttermilk mixture to a blender and add 4 tablespoons of the butter. Puree the mixture until very smooth and season with salt and pepper.
In a large skillet, melt 2 tablespoons of the butter. Arrange 6 of the endive halves cut side down in the skillet and season with salt and pepper. Cook over moderately high heat, turning, until nicely browned on both sides and crisp-tender, about 5 minutes. Repeat with the remaining 2 tablespoons of butter and endive halves.
In a medium bowl, combine the sliced raw endive with the halved olives, lemon juice and the remaining 2 tablespoons of olive oil and season with salt and pepper. Toss the endive to coat with the dressing.
Transfer the pork roast to a cutting board. Remove the strings and discard. Cut the meat crosswise into 4 thick slices. Spread the onion puree on plates. Arrange the endive halves on the puree and set a slice of pork on top. Scatter the endive salad over all and serve.