Heat oil in a large stockpot. Add onions and saute over low-medium heat until brown and caramelized, 25 or so minutes, stirring occasionally. Add garlic during the last 1 minute of this cooking time so it won't burn.
To the pot add ham hocks, bay leaves, chicken broth, both vinegars, sugar and pepper flakes. Bring to a boil, add Country Greens and stir to submerge. When the mixture returns to a boil, reduce heat, cover pot and boil gently for about 1 hour. Remove bay leaves. If you like, remove ham hocks from pot, cool them enough to handle them and then strip meat from hocks and add meat chunks back into the greens.