1 medium green, red or Savoy cabbage
¼ cup unsalted butter, softened
1 teaspoon finely grated lime zest (from 1 lime)
1 small garlic clove, finely grated
½ teaspoon smoked paprika
Hot sauce or red-pepper flakes, to taste
Olive oil, as needed
Heat the grill to medium-high.
Remove any wilted leaves from the cabbage, then cut through the root into 2-inch-thick wedges. Transfer to a large bowl or resealable plastic bag and add ¼ cup salt. Mix thoroughly with your hands to work the salt into the cabbage. Add 3 cups of water and stir to combine. Set aside, tossing occasionally, while the grill heats or up to 1 hour.
In a small bowl, use a fork to mash together the butter, lime zest, garlic and smoked paprika. Season to taste with salt and hot sauce.
When ready to grill, drain the cabbage and pat the outsides very dry. Drizzle with olive oil to coat. Clean the grill grates with a grill brush, then lightly grease the grates. Add the cabbage and cook, covered if using a gas grill, until the cabbage is floppy and deeply charred on all three sides, 6 to 10 minutes per side.
Transfer to a platter or plates. While still hot, spread the cabbage with the paprika-lime butter.
Recipe by NY Times