Heat the oven to 400°.
Add the peeled and quartered potatoes to a saucepan and cover with water (there should be about an inch of water between the potatoes and water's surface). Place over high heat and bring to a boil, then reduce the heat to bring it down to a simmer. Simmer the potatoes for 15 minutes, or until a knife easily slides through.
Drain the potatoes, reserving a half cup of the cooking water.
Return the potatoes to the saucepan and mash until chunky. Then add the water, 1 tablespoon ghee, ½ teaspoon fine sea salt and ¼ teaspoon black pepper. Keep mashing or whip with a wooden spoon or spatula until blended and fairly smooth. Set aside.
Meanwhile, while the potatoes are cooking, add 1 tablespoon olive oil or ghee to a medium, 10" heat-proof skillet and place over medium heat.
Once the oil is hot, add the onion and a pinch of salt and sauté, stirring occasionally until soft, about 10 minutes.
Add the ground beef or lamb and break it up as it cooks, stirring occasionally, until browned, about 10 minutes.
While the onion and meat cook, in a medium mixing bowl, whisk together the beef broth, coconut aminos and arrowroot. Set aside.
Once the meat is browned, add the thyme, rosemary, ½ teaspoon fine sea salt and ¼ teaspoon black pepper. Add the ½ cup of frozen peas and carrots and stir everything together. Cook until the peas and carrots are warmed through, about 2-3 minutes, stirring occasionally.
Give the broth mixture another whisk then pour it into the skillet and stir everything together.
Turn the heat up to medium high to bring the mixture to a boil, then reduce to a simmer and let it cook until thickened, about 10 minutes.
Spread the potatoes on the meat mixture. Distribute 2 tablespoons of ghee in little dabs over the potatoes.
Bake until the pie is hot and bubbly around the edges, about 30 minutes. Let rest for at least 10 minutes, then dig in!