Arrange a rack in the top third of the oven and another on the bottom third. Heat oven to 350 degrees.

Prep the cabbage: Remove any loose outer leaves, then cut the cabbage, leaving the core intact, into 8 equal wedges.

Drizzle 2 tablespoons of olive oil across the surface of a rimmed sheet pan, then sprinkle with ½ teaspoon kosher salt and a generous amount of pepper. Add the cabbage wedges and rub the bottom sides around in the oil to coat. Spread them out as much as possible with a cut-side facing down. Using a pastry brush (or your hands), rub the remaining 2 tablespoons of olive oil onto the tops and sides until well coated. Season with salt (about a heaping ½ teaspoon) and pepper to taste.

Roast on the lower oven rack for 50 to 55 minutes, until the bottoms are nicely browned and the tops are moderately browned.

Remove from the oven and increase the temperature to 425 degrees. Once at temperature, roast on the upper rack for 10 to 15 minutes, until deeply browned all over with some charring on the bottom. A paring knife inserted into the thickest part should yield minimal or no resistance.

Heat a medium frying pan over medium until hot, then add the peanuts and sesame seeds. Stir or shake the pan from time to time until the sesame seeds are golden brown and peanuts are a bit darker in color, 3 to 5 minutes. Transfer to a medium bowl.

Wipe out the frying pan and return to medium heat. Add the oil and once hot, add the mustard seeds and stir frequently. Once they just start to pop, add the curry leaves, if using, standing back as they may pop up vigorously. Stir for 15 seconds, then add the garlic and serrano chile and stir constantly for 1 minute, until the garlic just starts to turn color. Immediately pour into the bowl with the nuts and seeds.

To the bowl, add the dates, lime zest, 1 tablespoon lime juice and a pinch of salt. Mix together, then taste, adding more lime juice or salt as desired.

Cool the cabbage for a few minutes, then transfer to a serving platter. Drizzle with the tamarind and a bit more lime juice (it should taste tart and bright). Scatter the peanut crunch on top and serve.