In an 8-qt. pot, heat the oil over medium heat. Add the onion and cook, stirring frequently, until it begins to brown, 5 to 7 minutes. Reduce the heat to medium low and continue to cook until it’s softened and golden brown, 3 to 5 minutes more. Stir in the cayenne and cook for about 30 seconds.
Add the broth, the ham bone, and 1/2 cup water. Pile on the collards, cover with the lid ajar, and bring to a simmer over medium-high heat. Reduce the heat to medium low and simmer, stirring occasionally, for 30 minutes. Remove the lid and continue to simmer until the greens are very tender, about 15 minutes more.
Take the pot off the heat. Put the ham bone on a cutting board, and cover the pot to keep the greens hot. When the ham bone is cool enough to handle, pull off and shred or dice any meat clinging to the bone. Stir the meat into the greens, along with the vinegar. Season with salt, pepper, and more vinegar to taste. Pass the hot sauce at the table so diners can spice up the greens to their own tastes.