Preheat your oven to 300°F (150°C).
In a small bowl, mix the smoked paprika, chili powder, garlic powder, onion powder, sea salt, and black pepper to create the dry rub.
Coat the brisket evenly with the dry rub, pressing the spices into the meat on all sides.
Heat the olive oil in a heavy, oven-safe skillet or Dutch oven over medium-high heat.
Sear the brisket for 3-4 minutes per side until a dark, savory crust forms, then remove from heat.
Whisk together the apple cider vinegar, tomato paste, and maple syrup in a small jar, then pour the mixture over the seared brisket.
Cover the skillet tightly with a lid or double layer of foil and roast in the oven for 3 hours until the meat is tender enough to pull apart with a fork.
During the final 45 minutes of roasting, place the sweet potato half on a baking sheet and roast until soft.
Steam the green beans for 5-7 minutes until they are bright green and crisp-tender.
Allow the brisket to rest for 10 minutes before slicing against the grain, then serve with the roasted sweet potato and steamed green beans.