Core the cabbage and cut it into wide ribbons approximately 1 to 1.5 inches across, similar in width to pappardelle pasta. Pat the ribbons thoroughly dry with paper towels — surface moisture is the enemy of a good char.

Heat a large cast iron skillet or heavy stainless skillet over high heat until it is genuinely ripping hot, about 2 to 3 minutes. You should see the first wisps of smoke beginning to rise from the surface.

Add 1 tablespoon of the avocado oil and swirl to coat. Add half the cabbage ribbons in a single layer — do not crowd the pan. Season with half the salt and pepper and press down gently with a spatula. Cook undisturbed for 2 to 3 minutes until the undersides are deeply golden and charred in spots.

Toss and continue cooking for another 1 to 2 minutes until the cabbage is wilted and tender but still has a pleasant chew. Transfer to a large plate or bowl. Repeat with the remaining oil, cabbage, salt, and pepper. Set all charred cabbage aside.

Reduce the heat to medium-low. Add the butter to the same skillet and let it melt, scraping up any charred bits from the bottom of the pan — that's flavor.

Add the minced garlic and cook, stirring constantly, for about 60 seconds until fragrant and just barely golden. Do not let it brown or turn bitter.

Pour in the heavy cream and raise the heat to medium. Stir to combine and bring the cream to a gentle simmer. Cook for 3 to 4 minutes, stirring occasionally, until the cream has reduced by about one-quarter and is slightly thickened.

Remove the skillet from the heat. Add the freshly grated parmesan a small handful at a time, stirring constantly after each addition until fully melted and the sauce is smooth and glossy. Season with the remaining salt, black pepper, and nutmeg if using.

Return all the charred cabbage to the skillet with the Alfredo sauce. Toss gently to coat every ribbon in the sauce, using tongs or two wooden spoons. Place the skillet back over the lowest heat setting for 60 seconds just to warm everything through — do not boil.

Divide among warm shallow bowls. Top with fresh parsley, an extra grating of parmesan, a generous crack of black pepper, and lemon zest if using. Serve immediately.