Heat the olive oil in a large Dutch oven over medium-high heat. Sauté the chopped onion until it's a nice golden brown, then add the minced garlic and sauté for one minute, stirring constantly. Season with salt and pepper, then set aside.
Using the same pot, fry the cleaned, chopped collards in small batches over medium heat until they wilt. Put the wilted greens in a bowl and set aside.
Add the wilted greens back to the pot. Add the chicken stock, water, cooked onions, red pepper flakes, brown sugar, and vinegar, and stir until well combined. Place the ham hocks in the pot, making sure they are surrounded by the greens.
Cover and bring the pot to a boil, then turn it down and let it simmer for 1 ½ hours. Adjust salt to taste.
After 1 ½ hours of cooking, remove the ham hocks and let them cool for 45 minutes as the collards continue to simmer. Shred the meat, discarding any fat and gristle.
Add the ham hock meat to the pot. (Feel free to add an extra 1 cup of ham as well.) Simmer for 30 minutes, then adjust seasonings to taste.
Remove the greens from the pot with a large slotted spoon, being careful to reserve the liquid (potlikker) to enjoy as well. Pour the potlikker on individual servings of greens and sop it up with cornbread.
Serve the collards warm with cornbread, black eyed peas, or grits, or enjoy as a side dish along with other Southern favorites.