Preheat oven to 325°. Pat brisket dry with paper towels; season all over with salt and black pepper.

In a large Dutch oven over medium-high heat, heat oil. Add brisket and cook, turning occasionally, until browned, about 5 minutes per side. Transfer to a large baking dish.

Reduce heat to medium. In same pot, cook potatoes cut side down, undisturbed, until slightly softened, about 5 minutes. Add carrots and shallots; season with salt and black pepper. Stir to release potatoes. Return brisket and any accumulated juices to pot. Pour cider and broth over and add thyme and bay leaves. Add cayenne; season with salt and black pepper and stir to combine. Cover and bring to a boil.

Once boiling, transfer to oven, still covered, and roast until brisket is easily shreddable, 2 ½ to 3 hours.

Discard thyme and bay leaves. Shred brisket with 2 forks.

Transfer brisket to a platter. Arrange vegetables alongside and spoon juices over.