Season the pork. Preheat the oven to 350°F. Mix the flour with a generous amount of salt and pepper. Pat the roast dry and dredge it in the flour mixture.
Sear the pork. Heat the butter and olive oil in a large Dutch oven over medium-high heat until hot but not smoking. Sear the pork on all sides, 4 to 6 minutes per side, until golden brown and it releases easily from the pot. Move the pork to a plate.
Cook the vegetables. Reduce the heat to medium and add 1 cup of the chicken broth, scraping up the browned bits from the bottom of the pot. Add the carrots, onions, celery, and garlic. Cook, stirring, until the onions are translucent, about 10 minutes.
Bake. Place the pork on top of the vegetables. Add the remaining 1 cup of chicken broth, the apple cider, thyme, rosemary, and bay leaves. Season with salt and pepper, cover, and bake at 350°F for about 20 minutes per pound (about 80 minutes for a 4-pound roast). Start checking the pork at about 60 minutes, since thinner roasts cook faster.
Add the potatoes. With about 40 to 45 minutes of cooking time left, stir the potatoes into the liquid. Cover and return to the oven until the potatoes are fork-tender and the pork reaches 145°F. If the pork finishes first, remove it and let the potatoes keep cooking.
Rest. Let the pork rest for 10 to 15 minutes before slicing and serving.