Prep time 10 minutes
Cook time 15 minutes
Heat a heavy-bottomed skillet over medium heat. Add 2 tablespoons avocado oil.
Rinse cabbage under water. If any leaves fall off, cut those into 1/3-inch shreds. Arrange cut sides of large wedges down so nestled into the pan. Let cook, undisturbed, for about 7 minutes, until the bottom has browned. Carefully flip and cook for 3 more minutes.
Move cabbage to the edges of the pan, then add remaining avocado oil, any cabbage shreds, and sage to the center of the pan. Sauté and season with salt and pepper. Cook until wilted, about 3 minutes.
Push everything to the edges of the pan and place the walnuts in the center. Toast for about 2 minutes, moving them around to prevent from burning.
Transfer to a serving plate, adjust seasoning to taste, and finish with grated Parmesan, chives, and a drizzle of olive oil.