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 the cabbage in half from 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'll separate the cabbage into strips in your pan.)
Peel the garlic, cutting off the root and stem ends. Slice the garlic thinly.
In a 12-inch nonstick skillet (or use a cast iron pan if you have one), heat the olive oil on medium-high and add the garlic to the pan. Let the garlic cook for a couple of minutes before adding the sliced cabbage, salt and pepper. (It will look like too much, but the cabbage will cook down.) Stir the cabbage to coat it with oil, breaking up the cabbage into strips.
Let the cabbage cook, covered, on medium heat, stirring it occasionally. When you find the pan getting dry, add ⅛ cup of hot water. Continue letting the cabbage cook, stirring occasionally, until the cabbage is tender and getting brown. (Stir it less often to allow it to brown.) It will take at least 15 minutes, but depending on your pan, you may need 30 minutes. Don't let it burn. Taste the cabbage to see if it needs any more salt.
Store the leftovers in a sealed container in the refrigerator for up to four days.
Notes
If your head of cabbage is larger than two pounds, you will need to use more olive oil and garlic.