Using paper towels, pat the meat and marrow bones dry. Sprinkle generously with salt on all sides and let sit for 15 minutes.
Set a large, heavy-bottomed pot over high heat. Add 2 tablespoons of oil and sear the meat and bones on all sides until browned, about 2 minutes per side. Do not overcrowd the pot; work in batches. Transfer the meat and bones to a plate and set aside. If there are burnt bits on the bottom of the pot, quickly rinse it, but don’t scrub it clean; the browned bits add lots of flavor.
Return the meat and bones to the pot and cover with water. Bring to a boil over medium-high heat and skim off any scum that rises to the surface. Once no more scum rises, add the vegetables, bay leaves, and thyme. Add more water if needed to fully cover the vegetables. Bring back to a boil, then reduce the heat to low. Season with salt and pepper and cook for 4 hours. Place an upside-down plate over the contents of the pot to help keep everything fully submerged. Taste and adjust the seasoning occasionally, if needed. By the end of the cooking time, the meat should be fall-apart tender.
Strain the broth, reserving the meat and any vegetables you wish to keep, and discard the rest. Transfer vegetables and meat to containers, cover with broth, and refrigerate for a few hours or overnight.
Skim off and discard the solidified fat from the surface of the broth. Return the broth, meat, and vegetables to the pot and warm over low heat.
To serve, ladle hot beef broth into individual bowls and add the matzah balls. Serve the warm meat from the broth on a platter, along with Dijon mustard and pickles.
