Heat the vegetable or canola oil in a large Dutch oven or stock pot over medium-high heat. Once the oil shimmers, swirl the pot to coat the bottom evenly. Add the smoked meat (ham hocks or turkey wings) and cook until a golden brown sear appears, about 2-3 minutes per side.
Add the minced onion to the pot with the seared smoked meat and sauté, stirring often, until the onion is soft and tender, about 4-5 minutes. Stir in the minced garlic, red pepper flakes, kosher salt and ground black pepper to taste, 6 cups of chicken broth, and the hot sauce. Mix everything thoroughly to combine. Reduce the heat to medium-low, cover the pot with a lid, and let it simmer undisturbed for 1 hour. The smoked meat should become very tender and start to fall apart.
Carefully remove the smoked meat from the pot and set it aside to cool for a few minutes. Once it's comfortable to handle, use a fork or your hands (wear gloves if you like) to shred the meat from the bones. Discard the bones and any excess fatty parts. Return the shredded meat to the pot with the simmered broth. I always try to remove as much fat as possible for a cleaner, richer broth.
Add the brown sugar, apple cider vinegar, and collard greens to the pot. Stir thoroughly to mix all ingredients well. Don't worry if the greens seem to overflow—the collard greens will wilt down quite a bit as they braise. If you notice a low liquid level from simmering, add 1 to 2 more cups of chicken broth as needed for your preferred consistency. I like a generous amount of broth, sometimes called 'pot likker,' because it's absolutely packed with flavor.
Cover the pot and let the greens braise over medium-low heat for another 1 to 1½ hours, until the collards are tender and full of flavor. Taste the greens and adjust with more salt, pepper, and/or hot sauce according to your preference. Serve the collard greens warm, either on their own or as a flavorful side to your favorite main dish. Enjoy!