Wash and trim the brussels sprouts, removing any dingy looking leaves. Cut into quarters.
Place a skillet (cast-iron is ideal) over high heat. Once it is very hot, add the brussels sprouts to the dry skillet. Allow them to sear briefly, about 20 seconds and then drizzle in half of the olive oil. Shake the pan and cover with a lid. If the pan starts to smoke, lower the temperature. The brussels sprouts will continue to sear for another 1-2 minutes.
At this point, toss them gently in the pan then flip over any that were still stuck with a spatula. Add a bit more oil as needed. Cover with the lid and continue to sear. A bit of color should be on at least one side. Bite one brussels sprout. If it is not yet tender, but the color is a nice dark golden, then add a generous splash of water. Cover with the lid and steam until they are tender.
Once they are just about perfect, toss generously with the dukkah and salt. Taste. Add more dukkah if desired. Serve while still piping hot and steamy.