In a large pot, heat the oil until shimmering. Add the onions and garlic and cook over moderate heat, stirring occasionally, until softened, about 6 minutes. Add the chile powder and cayenne and cook just until fragrant, about 1 minute. Add the brown sugar and cook, stirring, until dissolved, about 1 minute longer. Add the ham hocks, chicken stock, sparkling cider and bay leaves. Season lightly with salt and pepper and bring to a boil. Reduce the heat to low, cover and simmer until the ham hocks are tender, about 2 hours.
Remove the ham hocks from the broth and let them cool slightly. Skim the fat from the broth. Remove the meat from the ham hocks and cut it into 1-inch pieces.
Bring the broth to a boil. Add the collards in large handfuls, allowing the greens to wilt before adding more. When all of the greens have been added, return the meat to the pot, cover and simmer until the collards are tender, about 30 minutes. Season with salt and pepper and transfer to a large bowl. Discard the bay leaves and serve.
Make Ahead: The braised collard greens can be covered with plastic wrap and refrigerated for up to 2 days.