Tip:Freezing is the secret to tender kale. Stuff washed kale in a heavy-duty zip-top bag and freeze it for a few hours or up to a month. Cook it straight out of the freezer. Freezing breaks down its fibers in a way that no amount of cooking can.
Remove the tough stems from the kale leaves by slicing a narrow “V” up into each leaf to remove the entire stem. Wash the leaves well in cold water and drain in a colander. Stuff into large (gallon-size or bigger) zip-top bags and put in the freezer for at least 2 hours or up to a month.
Fill an 8-quart pot with 2 inches of water and bring it to a boil over high heat, add a good pinch of salt, and add the frozen kale (yes, right out of the freezer). Cover with the lid slightly ajar and cook on high heat, turning occasionally, until tender, about 20 minutes. The kale should still have a little bite but shouldn’t be stringy or tough. Drain in a colander and press with the back of a large spoon to squeeze out as much excess liquid as possible. When the kale is cool enough to touch, chop it into small pieces.
Melt 3 Tbs. of the butter in the 8-quart pot over medium-high heat. Add the ham and cook until it starts to brown a little, about 3 minutes. Reduce the heat to medium. Add the onion and garlic and a pinch of salt; cook covered, stirring occasionally, until softened, about 5 minutes. You don’t want the onion or garlic to brown; if they start to, lower the heat. Add the broth, bring to a boil, reduce the heat to maintain a gentle simmer, and cook for 5 minutes. Return the kale to the pot, stir in the remaining 3 Tbs. butter, season generously with pepper (13 turns of a pepper mill should do), and cook gently until the flavors are well blended, about 7 minutes. Taste and adjust the seasonings as necessary.
Transfer to a serving bowl and serve immediately with a slotted spoon. Offer red-wine vinegar for sprinkling on individual portions, if you like.
This recipe can be made completely up to a day ahead: Just let it cool and then refrigerate; right before serving, reheat on the stove.