If you want, dredge the beef shanks through flour and coat it. ( I skip this to keep it lower carb)
Melt the butter in a large oven safe braising pan over medium to medium-high heat.
Fry the beef shanks in the butter until browned on the outside.
Remove the beef shanks to a plate, and keep warm.
Add the onion slices to the skillet; cook and stir until the onion is tender. Add in the garlic and the carrots and fry until the garlic is fragrant.
Pour in the white wine and deglaze the pan at this point. Stir in the beef broth and the tomatoes.
Return the beef to the pan, making sure the shanks are submerged in the sauce.
The best way to cook now is to place the lid on top and cook the shanks in a 300 °F for 4-5 hours, until the meat is tender and falling off the bone.
For stove top, cover and simmer on the stove top over low heat for 2-3 hours, checking and moving the meat occasionally to ensure that the bottom is not burning.
Notes
I keep this lower carb by NOT dusting the shanks in flour, you can dredge them through flour before frying them if desired.
I prefer my shanks to be velvety and falling apart, you can cook it until it's tender but the shanks remain together like a steak more. The choice is yours.
Serve with gremolata for a traditional dish.
This goes well over polenta, as is traditional as well