In a large skillet over medium-high heat, heat oil until shimmering. Saute onions, brown sugar, and 1-4 teaspoon salt (to taste) until onions are golden, 10 to 12 minutes. Clear a space in the middle of the pan. Add tomato paste and flour to open space and cook, stirring constantly, until darkened, about 2 minutes. Add garlic and cook until fragrant, about 30 seconds. Stir in broth and cook until sauce thickens, about 4 minutes. Off heat, stir in 2 tablespoons vinegar and transfer mixture to bowl. When cool, cover tightly with plastic and refrigerate.
Whisk together 1 teaspoon salt, paprika, onion powder, garlic powder, and cayenne in a small bowl. Prick brisket with fork, evenly all over both faces. Rub spice mixture over brisket and wrap tightly in plastic. Refrigerate brisket and onion mixture overnight.
The next morning, add half of onion mixture to slow-cooker. Add thyme and bay leaves and place brisket, fat side up, on top. Spread remaining onion mixture over brisket. Cover slow cooker and cook on low until brisket is fork-tender, 9 to 10 hours (or cook on high for 5 to 6 hours). If brisket it especially thick, cook an extra hour. Turn cooker off and allow brisket to rest for 30 minutes.
Remove brisket to cutting board. Cut across grain into 1-to-2-inch slices, and transfer to serving platter. Tent with foil.
Pour sauce into large skillet, discard herbs, and simmer over high heat until slightly thickened, 8 to 10 minutes. Skim off as much fat as possible, add remaining vinegar, then pour half of sauce over brisket. Serve with remaining sauce on side.