Heat the oil in a large cast-iron skillet over medium heat. Place half the Brussels sprouts, cut-side down, into the skillet. Without moving the sprouts, let them sear for 3 to 4 minutes, until deeply golden brown. Toss, sprinkle with half the salt and several grinds of pepper and continue to cook, stirring occasionally, for 5 to 6 minutes, until tender. Remove from the pan, add a little more oil, and repeat with the remaining sprouts.

When the second batch is finished, add the first batch back to the pan and heat until warmed through. Turn off the heat, squeeze with lemon, and season to taste with more sea salt or with flaky sea salt.

If desired, sprinkle with Parmesan or vegan Parmesan, and serve hot.