Heat the avocado oil in a large skillet over medium heat. Add the sliced onions and saute, stirring occasionally, until onions are translucent and begin to brown around the edges, about 15 to 20 minutes. Reduce the heat to medium-low and continue cooking, stirring occasionally, until onions have caramelized, about 30 to 40 minutes. Note: once the onions begin sticking to the skillet, de-glaze the pan with a few tablespoons of water - you'll likely need to do this 2 or 3 times.
While the onions are caramelizing, prepare the rutabagas. Peel the rutabagas and chop them into 2-inch cubes. Bring a pot of water to a full boil and add the chopped rutabagas. Boil for 20 to 25 minutes, until very tender.
Strain the rutabagas and place them in a high-powered blender or food processor. Add the remaining ingredients and blend until creamy. You will likely need to stop the blender/food processor a few times to scrape the sides to help the blending along. Note: if you don't own a high powered blender or food processor, simply transfer everything back into the pot you used for boiling and mash it all together using a masher.
Taste mashed rutabaga for flavor and add more ghee, coconut milk, and/or sea salt to taste. Serve with your favorite entree.