Strip cabbage of its outer leaves; rinse the head well and pat dry.
Now slice the cabbage in half through its tough, fibrous core with a long, sturdy knife.
Cut each half in half again through the core. This will expose the core to make it easy to remove.
Holding each cabbage quarter upright, remove the tough core.
Now you can slice the cabbage into long, thin strips for slaws, salads, soups or stews or thicker strips for braises and sautés.
Onion slices are versatile. In quick-cooking dishes, they stay distinct enough from the other ingredients that they don't permeate every bite as diced onions would. In longer-cooking dishes, they have enough surface area to turn soft and brown, but their natural shape and length keeps them intact.
To make contoured half-round slices, first cut the onion in half through the root.
Next, slice away the both ends of each half and pull away the onion's skin. Since the ends hold the slices together, cutting them off frees the slices to fall into individual pieces.
Starting on one side of the onion with the knife at an angle, make slices as thick or thin as you like.
Rotate the knife around the contour of the onion, bring it closer to perpendicular to the cutting board as you go.
Choose cabbages that look fresh and healthy -- with no wilted or limp leaves, slime, black or brown spots or blemishes.
The leaves of firm green or red cabbages should be compact and tight; the leaves of softer cabbages like Savoy and Napa should look healthy and crisp with well-defined veins in their leaves.
All cabbages should feel heavy for their size.
