Heat the Dutch oven over medium-high heat and add olive oil. Once shimmering, add beef chunks and sear until all sides are golden brown, about 4-5 minutes per batch. Remove beef and set aside.
Add chopped onion, carrots, and celery to the same Dutch oven. Sauté until vegetables are softened and onions are translucent, about 5-7 minutes. Stir in minced garlic and cook for another minute until fragrant.
Sprinkle flour over the vegetables and stir to combine. Cook for 1-2 minutes to eliminate raw flour taste. Pour in apple cider, scraping the bottom of the pot to deglaze and incorporate browned bits, until the mixture begins to thicken slightly.
Return the browned beef to the pot, along with any accumulated juices. Season with salt and black pepper. Cover the Dutch oven with a lid and reduce heat to low. Let it simmer gently for 2.5 to 3 hours, until the beef is tender and falling apart, with vegetables soft and flavorful.
Remove the lid and increase heat slightly to allow the sauce to reduce and thicken further, about 10-15 minutes. Stir occasionally, and check for desired consistency. Taste and adjust seasonings as needed.
Serve the pot roast hot, with shredded meat and vegetables on a plate, spooning over the rich cider sauce. Garnish with fresh herbs if desired.
