Heat oven to 325 F. In large heavy pot, heat oil over medium-high heat. Season both sides of brisket with salt & pepper. When oil shimmers, add the brisket fat side down and cook until dark golden, 3-4 minutes. Flip and repeat to brown other side. Remove meat from pot and add onions, garlic, & thyme. Cook until onions soften, about 4 minutes. Stir in tomato paste and 4 cups of water and bring to a simmer. Return brisket to pot, fat side up; cover and transfer to the oven. Cook until almost tender, 2 hours 45 minutes. Add the vegetables, submerging them slightly in cooking liquid. Continue cooking until all veggies are tender, about 30-45 additional minutes. Slice brisket against the grain and serve with the vegetables and sauce.