Preheat the oven to 325°F.
In a small bowl, combine the flour, garlic powder, salt, and black pepper. Coat the venison neck lightly with the seasoned flour and set aside.
Heat a 6–7 quart cast iron Dutch oven over medium heat and add the oil. When hot, carefully add the floured meat and brown for about 5 minutes per side. Remove the meat and set aside.
Add the carrots, celery, onions, and garlic to the pot. Cook until the onions soften, about 7–8 minutes. Partially covering with a lid can help the vegetables soften faster.
Pour in the beef broth and wine, stirring to loosen any browned bits from the bottom of the pot. Return the neck meat to the pot and add the tomato paste and bay leaves.
Cover the pot, leaving a small opening for steam to escape, and place in the oven. Braise for 6–7 hours, basting every 2 hours and adding more liquid if needed. During the last 30 minutes, add the cinnamon stick. The longer you braise, the more tender the meat will become.
Carefully remove the meat and shred on a cutting board. Serve over mashed potatoes, spooning the rich braising liquid over top. Garnish with chopped green onions and parsley if desired.
Slow Cooker Tip: After browning meat and cooking vegetables, transfer everything to a slow cooker. Add tomato paste and bay leaves, and cook on low for 6–8 hours.