In a small bowl, combine the tomato paste, brown sugar, vinegar, Worcestershire sauce, mustard, and garlic.
If the meat is too big to lie flat in you slow cooker, cut it in half; season the meat generously with salt, pepper, and paprika.
In a large nonstick skillet, heat the oil over high heat; when oil is hot, brown the brisket very well, about 3 minutes per side; transfer to a plate.
Add the onions to the skillet and cook, stirring a few times, until browned or even a bit blackened on the edges, 5-7 minutes.
Put half the onions in the slow cooker (if you have cut the brisket into 2 pieces, place 1/3 of the onions in the cooker).
Smear the tomato paste mixture thickly on both sides of the brisket and place in the cooker, with the fattier side facing up.
Top with the remaining onions (if you have cut your brisket into 2 pieces, place 1/3 of the onions between the two pieces of brisket, and the remaining onions on top of the second piece).
Pour any meat juices from the plate over the brisket.
Cover and cook on LOW 5-7 hours, until the brisket is tender when pierced with a fork.