This dish is my Italianized version of an old Cuban classic (ropa vieja, which means "old clothes" since the finished product looks a bit like rags) and it's extremely easy to make, tastes glorious and is adaptable to seasonal variations.
Poach it at as low a heat and as long a time as you have patience for; the liquid should barely bubble. If you have a slow cooker, even better...let it poach overnight. You want to melt the connective tissue in the brisket so that this will be VERY readily shredded. Reserve the broth to make stocks, soups, etc. Put the garlic and onion in a small saucepan over medium-low heat with the extra virgin olive oil and saute until the onion is golden, making sure you don't color the garlic too much. Add the basil or oregano and tomatoes. Season w. salt and pepper. Cook until it coats the back of a wooden spoon.
Shred the beef with two forks into long, spaghetti-ish strands. Toss in sauce, as if this was a linguine or spaghetti dish. Top with Parmigiano-Reggiano (Asiago works great, too) cheese, if desired. Other worthwhile options include crumbled pancetta and chile flakes, or porcini mushrooms reconstituted in Marsala or the beef broth.
Leftovers can be reheated and topped with buffalo mozzarella to make a terrific sandwich/panino; they can be topped with polenta to make an interesting variation on shepherd's pie or even folded over into a calzone. You can even add back a bit of the beef broth to make this more of a soup/stew thing.