GARNI: Prepare the bouquet garni: Place seasonings into middle of cheesecloth and tie with twine. Set aside.
BEEF: The method of tying up the brisket is optional for presentation, if not rolling, be sure and place brisket fat side up in the pot. TO ROLL, roll up the brisket fat side out into a cylinder shape and tie securely with twine. Place tied beef into a pot. Cover with cold water, add cider vinegar (the vinegar helps tenderize the meat), and bring to a boil. Remove the scum off the surface as it appears. Reduce the heat and simmer for 10 minutes. If the liquid is salty after 10 minutes, start again with boiling water. Add bouquet garni. Simmer for 2-3 hours skimming any scum as it appears on the surface.
VEGETABLES: Transfer beef to a large clean pot. Strain the liquid, cool slightly, and remove any oil/grease. Add onions, turnips, potatoes, carrots and cabbage, and apple cider to the pot containing the brisket. Cover with strained liquid and cook at a simmer for 1 hour more, or until very tender (you can pierce beef easily with a skewer).
SERVE: Remove the meat from the poaching liquid , cut the trussing strings and carve the meat into generous slices. Place them on a warmed platter. Arrange the cooked garnish vegetables around the meat. Sprinkle with chopped fresh parsley and serve with the beets.