Add the potatoes to a medium sauce pan and cover with water. Add 1 teaspoon salt, partially cover with a lid and set over high heat. Bring the water to a boil and cook, until the potatoes are fork-tender. Drain the water and add the chicken broth, 2 tablespoons olive oil and ½ teaspoon salt. Mash the potatoes with a potato masher until smooth and combined. If the potatoes are dry, add more chicken broth and olive oil as needed. Taste for seasoning and adjust with salt as desired. Cover and set aside in a warm place.
Preheat Traeger Grill to 450F or oven to 400F.
Heat a 12” oven-safe pan over medium-high heat. Add 2 tablespoons olive oil and heat until shimmering. Pat the ground beef dry with paper towel and form into large meatballs. Add the ground beef to the pan and cook until browned, around 5 minutes. Flip and brown the bottom sides, around 4 minutes. Reserve 2 tablespoons of rendered fat in the pan and transfer the browned beef to a bowl. Crumble the beef into small pieces with a potato masher or wooden spoon. Set aside in a warm place.
Lower the heat to medium. Add the carrot, celery and onion and season with a pinch of salt. Cook, stirring regularly, until the onion is soft and translucent, around 5 minutes. Add the mushrooms and cook, stirring regularly, until they have softened, around 7 minutes. Add the garlic and cook, stirring, until fragrant, around 60 seconds.
Add the arrowroot starch and onion powder and cook, stirring, 60 seconds. Add the tomato paste and cook, stirring to incorporate, 60 seconds. Add the beef broth and cook, lifting any brown bits off the bottom of the pan, until the liquid starts to simmer. Return the browned beef to the pan, add the frozen peas, season with black pepper to taste and cook, stirring occasionally, until the liquid has reduced by half, around 12 minutes. Taste the filling for seasoning and adjust with salt and pepper as desired.
Remove the pan from the heat, spoon the mashed potatoes overtop, spread evenly with a spoon and drizzle the top with 2 tablespoons olive oil. Transfer the Cottage Pie to the Traeger Grill or place onto a rimmed baking sheet and transfer to the oven. Bake until the mashed potatoes are golden and slightly crispy, 35 to 40 minutes. Remove from heat, garnish with chopped parsley and let cool 15 minutes before serving.