Preheat oven to 350°F. Using the coarse grater disk on a food processor or the largest holes on a box grater, shred potatoes. Toss with 1 tsp. salt and ½ tsp. pepper in a large bowl.
Transfer to a clean dishtowel, gather together ends of towel, and thoroughly wring out excess liquid over the sink; Transfer potatoes to a bowl and set aside.
Heat 1 tablespoon coconut oil in a 10" cast iron skillet and cook the sausage, until browned and barely cooked through. Don't overcook. Remove from heat and set aside. Heat 2 tablespoon coconut oil in same skillet and add onion and butternut squash. Cook until beginning to soften, 5-6 minutes. Set vegetables aside.
Using the same skillet, heat avocado oil over medium-high. Add potatoes and immediately start forming into a crust by pushing potatoes flat against bottom and sides of pan. Continue cooking, pressing potatoes up sides of pan if they start shrinking, until potatoes are bound together and bottom of crust is starting to brown, about 10 minutes. Remove pan from heat and set aside.
Whisk eggs, coconut milk, mustard powder, nutmeg, remaining ½ teaspoon salt, and remaining ¼ teaspoon pepper in another large bowl. Whisk in herbs and set aside.
Pour in onions and butternut squash evenly over bottom of potato crust, then layer sausage and lastly pour in egg mixture. Bake until quiche is set and crust is well browned, 30-35 minutes. Let cool to room temperature before cutting into wedges and serving from the pan.