While it may be tempting to just dig out a cabbage core with the same butcher knife you plan to use for slicing the cabbage, that's not a good idea. Rather than putting yourself in danger of a slipping knife, take a few extra minutes to cut the cabbage before coring. Cabbage is long lasting and keeps for up to a week in the refrigerator, so only slice as much as you need for one meal and save the other cut pieces for later in the week.
Peel off the loose outer leaves that comprise the outer layer of the cabbage with your fingers. Take off as many layers as you need to, as many as 2 or 3, so only fresh-looking, unblemished leaves remain.
Wash the cabbage under running water and pat it dry. Although cabbage appears on the Environmental Working Group's list of the "Clean Fifteen" group of vegetables that have the smallest amount of pesticide residues, you still need to wash it thoroughly as you would any vegetable.
Cut the cabbage in half and cut each half into quarters if you plan to use the entire head. If you use only one or two quarters, store the extra quarters uncored and wrapped in a plastic bag in the refrigerator, poking a few holes in the bag to let any extra moisture escape.
Hold one quarter of the cabbage head slightly upright with the bottom of the core resting on the cutting board. Use a cutting board that is completely steady as it sits on your counter and that is large enough to give you plenty of space for cutting.
Place a butcher knife at a diagonal angle to the core and slice it off, beginning near the top of the core and slicing downward toward the bottom of the core and the cutting board. If you haven't cut deeply enough to remove the entire core, repeat the process until you've removed it all.