- Trim outer fat of brisket to about 1/4 in., then pat dry. Heat oil in a large frying pan over medium-high. Add brisket and brown all over, 10 to 15 minutes. Place in a 5- to 6-qt. slow-cooker.
- Swirl butter into frying pan, then add onions and carrots. Cook, stirring often, until onions are lightly browned, about 10 minutes.
- Stir in paprika, Worcestershire sauce, pepper, mustard, and 1/2 tsp. salt.
- Pour in broth, increase heat to high, and scrape up browned bits. Reduce heat and simmer 5 minutes to combine flavors.
- Pour vegetables and broth over meat. Cover. Turn heat to low (meat should simmer gently but not boil) and cook until meat is tender when pierced with a fork, 6 to 8 hours.
- Lift meat to a platter, cover with foil, and let rest 15 minutes.
- Pour sauce into a large frying pan and boil over high heat until reduced to about 1 cup.
- Slice brisket across the grain, top with parsley, and serve with sauce.