Separate the leaves of the Swiss chard from the stems. Thinly slice the stems. Chop or tear the leaves into large, 2-inch pieces. Rinse and blot dry if necessary.
Heat the oil in a 12-inch skillet over medium-high heat. Add the chard stems and cook, stirring occasionally, until softened, about 4 minutes. Add the leaves to the pan one handful at a time, stirring to coat, until they are wilted enough to add the next batch. When all of the chard has been added, cook until tender, stirring occasionally, about 5 minutes.
Remove the chard to a colander and allow it to drain, pressing as much additional liquid out as possible. (You can press with the back of a spoon or a clean kitchen towel once the chard has cooled slightly.)
Wipe out the skillet, add the half-and-half and simmer until reduced to 1/2 cup and very thick, about 5 minutes. Stir in the Parmesan and black pepper. Add the chard back to the pan and stir to coat. Taste, and season with salt.
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