Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions until al dente. Before draining, reserve about 1/2 cup of the starchy pasta water. Drain the rest and set the pasta aside.

While the pasta cooks, melt the butter in a large skillet or pan over medium-high heat. Add the thinly sliced cabbage. Sauté the cabbage for about 7 to 8 minutes, stirring occasionally, until it becomes tender and starts to turn golden brown at the edges. Stir in the minced garlic and cook for another 60 seconds until fragrant.

Lower the heat to medium-low. Pour the heavy cream into the skillet with the cabbage. Stir in the lemon zest, lemon juice, salt, and pepper. Let the mixture simmer gently for 2 to 3 minutes until it begins to slightly thicken. If the sauce seems too thick, add a splash of the reserved pasta water to reach your desired consistency.

Add the cooked pasta directly into the skillet with the creamy cabbage sauce. Use tongs to toss everything together, ensuring every strand of pasta is coated. If you are using Parmesan cheese, sprinkle it in now and toss again. Serve immediately in warm bowls with an extra sprinkle of lemon zest or red pepper flakes if you like a little heat.