Bring 2 quarts of water to a boil in a 6- to 8-quart wide heavy pot. Add cabbage and simmer, covered, until tender, about 10 minutes.
Transfer cabbage with tongs to a colander reserving cooking liquid, then add half of mustard, turnip, and beet greens and kale to cooking liquid. Simmer uncovered, 5 minutes.
Transfer greens with tongs to colander with cabbage, then cook remaining greens in same manner and transfer to colander.
When greens are cool enough to handle, finely chop.

Add ham hocks and andouille to cooking liquid (liquid will not cover them completely) and simmer, covered, 1 hour.
Transfer with tongs to a cutting board to cool.
Transfer ham broth to a bowl, adding water if necessary to measure 5 cups liquid.
Discard skin, bones, and fat and finely chop ham.

Cook onions and garlic in butter in pot over moderate heat, stirring frequently, until golden, about 5 minutes.
Add flour and cook, stirring, 3 minutes.
Add ham broth in a slow stream, stirring constantly.
Add chopped greens, ham, thyme, and minced chile and simmer, uncovered, until greens are tender, about 8 minutes. 
Gradually add spinach, stirring until wilted.
Stir in parsley, vinegar, and salt.
Serve with hot sauce and additional vinegar if desired.