Heat the avocado oil in a large 12-inch skillet that has deep walls and a lid over medium-high heat.
Add the sliced onion and sauté, stirring occasionally, until the onion begins to brown, about 5 to 8 minutes.
Add the sliced cabbage and cover. At first, this will be a ton of cabbage but after the cabbage steams for a few minutes, it will begin to wilt and become easier to stir.
Cook the cabbage, stirring occasionally, until it has fully wilted, about 15 to 25 minutes. The cabbage will begin to caramelize and turn golden-brown - this is a good thing!
Add the remaining ingredients and stir well. Cook, stirring frequently, until cabbage has reached desired doneness and much of the sauce has evaporated, about another 8 to 10 minutes longer.
Serve curry sautéed cabbage as a side dish with lemon wedges, or add your favorite animal protein to turn it into a main entrée.