Preheat the oven or Traeger grill to 425F.
Place the potatoes on a rimmed baking sheet lined with parchment paper and use a fork to poke a few holes all around. Lightly drizzle the potatoes with olive oil, massage them to coat and season generously all over with salt. Transfer the potatoes to the oven or Traeger and cook until the potatoes are completely fork-tender, around 1 hour.
Meanwhile, heat a sauté pan over medium heat. Add 1 tablespoon of butter and 1 tablespoon of olive oil and heat until the butter has melted. Add the carrot, celery and onion and season with a pinch of salt. Cook, stirring, until the onion is soft and translucent, around 5 minutes. Add the mushrooms and cook, stirring, until softened, around 5 minutes. Add the ground lamb and cook, crumbling it with a spatula, until no longer pink, around 10 minutes. Add the chopped garlic, rosemary, onion powder and tomato paste and cook, stirring to incorporate, around 60 seconds. Add the beef broth and cook, lifting any brown bits off the bottom of the pan, until the liquid starts to simmer. Add the frozen peas, season with 1/4 teaspoon black pepper and cook, stirring, until the liquid has reduced by 1/4 in volume, around 10 minutes. Taste for seasoning, adjust with salt and pepper as desired and set aside.
Once the potatoes are fork-tender, use a sharp knife to cut an oval-shaped opening in the top of each potato. Using a spoon, carefully scoop out the potato flesh, leaving the skin in tact, and transfer it to a bowl along with the Greek yogurt, all but 4 tablespoons of the grated cheese, 2 tablespoons melted butter, 1/4 cup beef broth, 1/4 teaspoon salt and 1/8 teaspoon black pepper. Mash everything together with a potato masher until smooth yet slightly chunky, adjusting with more beef broth as needed.
Fill each hollowed out potato with the ground lamb mixture and top each with 1/3 cup of mashed potatoes. Garnish each potato with around 1 tablespoon of grated cheese, place them back onto the sheet pan lined with parchment paper, transfer to a 425F oven or Traeger and cook until the mashed potatoes are golden brown and the cheese has melted, around 35 minutes.
Garnish the potatoes with green onion and serve with a side salad or grilled vegetables of choice.