Heat the avocado oil and bacon grease in large rondeau pot or dutch oven over medium-high heat. Add the ribs and cook each side for approximately two minutes, until browned all over. Transfer the ribs to a plate and set aside.
Add the onions, shallot and garlic to the pot and cook for 3-4 minutes or until the onions become translucent. Stir in the wine and cook for 5 minutes, to reduce the wine by approximately half.
Place the ribs back in the pot and add the beef broth and herbs. Cover, reduce the heat to low and cook for 2 to 2.5 hours, until the meat is very tender.
Remove the ribs to a plate. Strain the sauce through a fine sieve into a bowl and discard the solids. Place the sauce back in the pot and simmer for 15 minutes, to reduce the sauce further. Add the ribs back to the sauce and cook for 5 minutes, until warmed through.
While the sauce is simmering, make the root vegetable mash. Bring a large pot of water to a boil and add the diced parsnips and turnips. Cook for 15 minutes, or until fork tender. Strain the root vegetables into a colander.
Heat the olive oil in the same pot used for the vegetables over medium heat and add the garlic. Cook for 1 minute and add the butter, stirring until melted. Turn off the heat, add the root vegetables back to the pot and use a potato masher to mash the vegetables. Add the rosemary, salt and pepper and stir until well combined.
Serve a large spoonful of root vegetable mash with 1-2 short ribs. Garnish with parsley.