To flush out some of the sodium from the corned beef brisket, place your brisket in a large pot and cover it with cold water. The water should be a couple inches higher than the meat. Place the pot on the stove, cover it and heat it on high, just until the water boils.
When the water boils, turn off the heat and carefully transfer your corned beef to a platter. Drain the water from your pot.
Place the corned beef back in your pot and cover the beef with hot water, until the water is about three inches higher than the meat. Add the contents of your seasoning packet to the pot and cover it. Heat the pot on high, and when the water boils, lower the heat to let the pot simmer.
Simmer your corned beef, covered, for 50 minutes per pound, until it is fork tender - mine took two hours and 25 minutes.
When it is tender, carefully transfer the beef to a clean platter (you can wash the first one before using it again) and keep the cooking liquid for now. Let the corned beef cool off at room temperature for 20-30 minutes before slicing it thinly against the grain. (Slice the meat on the diagonal in the opposite direction of the flow of lines in the meat.) Pour a little of the cooking liquid over the meat, but note the liquid will be salty, so don't use too much. Reserve some of the cooking liquid in a small covered container to use as needed.
Allow an hour to make your cabbage. Rinse the head of cabbage and pat it dry. Remove a few of the outer, dark leaves. On a large cutting board, slice off the root end and discard it. Cut your cabbage in half from the top to bottom, then cut those pieces in half, cutting out and discarding the core. Take each quarter of cabbage and slice it into wedges about half an inch thick. Cut those in half if they're large. (You will separate the cabbage into strips in your pan.)
Peel your garlic, cutting off the root and stem ends. Slice the garlic thinly.
If you have an extra-large skillet, use it, or else you'll need two 12-inch skillets. Heat your olive oil in the skillet(s) on medium high and add the garlic to the pan(s). Let the garlic cook for a couple minutes before adding your sliced cabbage, salt and pepper. Stir the cabbage to coat it with oil, breaking up the cabbage into strips. (If using two pans, you may need to add more olive oil to coat the cabbage.)
Let the cabbage cook, covered, on medium heat, stirring it occasionally. When you find the pan getting dry, add a little hot water. (I used ⅛ cup in my extra-large skillet.) Continue letting the cabbage cook, stirring occasionally, until the cabbage is tender and getting brown. Mine took 45 minutes, but it will depend on your pan. Don't let the cabbage burn. Taste the cabbage to see if it needs any more salt.
Serve thin slices of corned beef with the cabbage. Store the leftovers in the refrigerator for up to five days.
The seasoning packet comes in the package of corned beef. The packet usually contains peppercorns, mustard seeds and bits of bay leaf.
I used a 2-pound head of savoy cabbage, which is smaller than the green cabbage. If your head of cabbage is larger than two pounds, you will need to use more olive oil and garlic.
The sodium in this dish is much less than what is calculated in the nutrition info, since we are boiling the corned beef first to flush out some of the sodium.