Step 1: Bring a large pot of generously salted water to a boil. Cook pasta until just al dente according to package instructions, reserving 1/2 cup starchy water before draining.

Step 2: While pasta cooks, heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the sliced cabbage in an even layer. Cook 8–10 minutes, turning occasionally, until tender with browned edges.

Step 3: Reduce the heat to medium. Add remaining butter, garlic, black pepper and optional red pepper flakes. Stir for 30–60 seconds until fragrant.

Step 4: Add heavy cream and bring to a gentle simmer, then reduce heat to low. Add Parmesan gradually, stirring until smooth; do not boil the sauce after adding cheese.

Step 5: Add drained pasta and toss vigorously. Splash in reserved pasta water, one tablespoon at a time, until the sauce clings silkily to the noodles.

Step 6: Finish with lemon juice, taste and adjust salt. Serve immediately with more Parmesan and black pepper if desired.