Prep the pork: Preheat the oven to 350°F. Pat the pork dry with paper towels and season on all sides with salt and pepper.
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, turning every couple of minutes, until golden brown on all sides, about 8 to 10 minutes total. It doesn't need to cook through. Remove to a plate.
Cook the vegetables: Reduce the heat to medium. Add 1 cup of the chicken broth and scrape up the browned bits from the bottom of the pot. Add the potatoes, carrots, onion, celery, and garlic. Cook, stirring, until the onions are translucent, about 10 minutes. Season with salt and pepper.
Bake covered: Place the pork on top of the vegetables. Add the remaining 1 cup of chicken broth, the apple cider, thyme, rosemary, and bay leaf. Cover and bake at 350°F until the pork reaches 140°F to 145°F, about 20 to 25 minutes. Move the pork to a plate and tent with foil.
Finish the vegetables: Increase the oven to 400°F. Return the covered pot to the oven and roast the vegetables for about 15 more minutes, until fork-tender.
Slice and plate: Use a slotted spoon to move the vegetables to a serving platter. Slice the pork, arrange it on top, and tent with foil to keep warm.
Make the gravy (optional): Strain the juices from the pot and wipe the pot clean. Melt the butter over medium heat until bubbly. Whisk in the flour and cook for 30 seconds. Gradually whisk in the strained juices until the gravy reaches the consistency you like. Let it bubble for 1 to 2 minutes, then season with salt and pepper.
Serve: Spoon the gravy over the pork and vegetables.