Preheat oven to 350 degrees. In a large Dutch oven or heavy pot, heat 2 tablespoons oil over medium-high. Season brisket with salt and pepper; in batches, cook, turning occasionally, until dark brown on all sides, about 20 minutes total. Transfer brisket to a plate and discard fat from pot. Return pot to heat and add 2 teaspoons oil and shallots; cook, stirring, until shallots are browned, 3 minutes. Add garlic and cook, stirring, until fragrant, 1 minute.
Add wine and simmer rapidly until reduced by three-fourths, about 15 minutes. Return beef to pot and add just enough water to cover meat (5 to 6 cups). Bring to a boil, cover, then place pot in oven. Cook until beef is tender, 3 1/2 to 4 hours.