Preheat oven to 400 degrees F. Heat a large cast iron skillet over medium-high heat. Toss the Brussels sprouts in a large bowl with 2 tablespoons of the oil. Season with 1 teaspoon salt.
Place the sprouts cut side down in the skillet and let brown, 2 to 3 minutes. (Don't crowd the sprouts, if you have to, brown in 2 batches, removing the first batch to a plate.) Once the sprouts are browned, toss in the skillet and roast in the oven for 5 minutes. Remove and toss with the chili flakes and the remaining tablespoon of the oil. Roast until tender, 6 to 7 minutes. As soon as the sprouts are out of the oven, sprinkle with the lemon zest and squeeze the lemon half over the top. Toss well. Sprinkle with flaky sea salt and serve.