Fill a large sink or basin with cold water and submerge the collard greens, swishing them around to loosen any dirt or grit. Lift the greens out of the water, leaving any sediment behind, and repeat this rinse two to three times until the water runs clear.
Fold each leaf in half lengthwise along the thick center stem and use a sharp knife to cut the stem away, discarding it. Stack several leaves at a time, roll them into a tight bundle, and slice crosswise into wide ribbons about one inch thick.
Set your Dutch oven over medium heat and add the bacon grease or vegetable oil, letting it melt and shimmer. Add the diced onion and cook for about 5 minutes, stirring occasionally, until it turns soft and translucent.
Stir in the minced garlic and cook for another 30 seconds, just until fragrant, being careful not to let it burn.
Push the onions to the side of the pot and add the ham hocks directly to the hot surface. Sear the ham hocks for 2 to 3 minutes per side, turning with tongs, until the skin picks up a bit of color.
Pour the chicken broth into the pot, scraping up any browned bits from the bottom with your wooden spoon. Add the apple cider vinegar, sugar, and red pepper flakes if using, and stir to combine. Bring the liquid to a gentle boil over medium high heat.
Once boiling, reduce the heat to low, cover the pot, and let the ham hocks simmer for 45 minutes. This gives the meat time to start releasing its smoky flavor into the broth before the greens go in. Check occasionally to make sure the liquid stays at a gentle simmer, not a rapid boil.
Add the chopped collard greens to the pot in batches, stirring each batch down as it wilts to make room for the next. Once all the greens are in the pot, make sure they are mostly submerged in the broth, adding a splash of water if needed. Season with a pinch of salt and black pepper, keeping in mind the ham hocks will add saltiness as they cook.
Cover the pot again and reduce the heat to maintain a low simmer. Cook for 45 minutes to 1 hour, stirring every 15 minutes or so, until the greens are completely tender and no longer tough or fibrous. Taste the pot liquor partway through and adjust the salt, pepper, or vinegar as needed.
Remove the ham hocks from the pot using tongs and set them on a cutting board to cool slightly. Once cool enough to handle, pull the meat away from the bone and skin, discarding anything you don't want to eat. Shred the meat into bite sized pieces and stir it back into the pot of greens.
Give the greens one last taste and adjust the seasoning with additional salt, pepper, or a splash more vinegar if you like a brighter finish. Ladle the greens into bowls along with plenty of the pot liquor. Serve hot, ideally with a side of cornbread for dipping.