Pat the beef dry and season it with salt and pepper. If necessary, you can tie the beef with kitchen string to help it keep its shape during cooking.
In a large Dutch oven over medium-high heat, warm the olive oil. Add the beef and sear, turning as needed, until a browned crust develops all over, about 5 minutes per side. Remove the beef from the pot and reduce the heat to low.
Toss the onion, carrot, and celery into the pot along with a good pinch of salt and half the butter and gently cook until the vegetables are soft and translucent, 8 to 10 minutes.
Return the beef to the Dutch oven, add the garlic cloves and herbs, and then pour in the wine. Season with salt and pepper. Increase the heat to medium-high, bring the wine to a boil, and let it simmer rather fiercely for about 5 minutes.
Pour in the stock. Ideally, you should have enough to cover the meat or almost cover it. Bring the liquid back to a boil, cover with a tight-fitting lid, and reduce the heat to low. Let it simmer gently, turning the beef occasionally, until the beef is very tender, 2 1/2 to 3 hours. Alternatively, you can slide the braised beef in an oven preheated to 320°F (160º) for the same amount of time.
Transfer the meat to a cutting board and let it rest while you finish the sauce. Remove and discard the bay leaves and rosemary or thyme stalks, if you used them.
Using an immersion blender, blitz the vegetables and liquid until smooth. (Alternatively, you can carefully transfer the hot liquid and its contents to a blender, blitz until smooth, then return to the pot.)
Reduce the sauce over medium heat, uncovered, until slightly thickened, about 30 minutes. Drop in the rest of the butter and swirl it through the sauce until glossy. Taste for seasoning, adding salt and pepper if necessary.
Cut the beef into slices about 1/2 inch (12 mm) thick and return them to the sauce. (If you wish, you can let the entire pot of beef and sauce cool and then refrigerate it overnight or for up to 3 days. Before serving, skim any fat from the surface, bring it back to a simmer on the stovetop, and then let it warm, uncovered, for about 10 minutes.)
Sprinkle with parsley and serve immediately.