Remove lamb from fridge 1 hour before cooking and let come to room temperature. Pat the meat very dry with paper towel and form into large ball shapes. This will help with the browning process.
Heat a large skillet or sauté pan over medium-high heat. Add avocado oil and heat until shimmering. Add the ground lamb and cook until browned, around 5 minutes. Flip and brown the bottom sides, around 4 minutes. Reserving the fat in the pot, transfer the lamb meatballs to a bowl and set aside.
Lower the heat to medium. Add the celery, carrot 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 zucchini and garlic and cook, stirring, until the zucchini has slightly softened, around 5 minutes.
Add the smoked paprika, sweet paprika, and onion powder. Cook, stirring to combine, until spices are fragrant, around 60 seconds. Return the browned lamb to the pot and stir to coat. Add the chicken stock and season with pepper and 1 teaspoon salt. Raise the heat to medium-high and bring to a steady simmer. Cook, uncovered, 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 from heat, add the parsley and stir through. Transfer filling to a casserole dish, if using. Otherwise, leave it in the skillet and spoon the mashed yams topping over top and spread it out with a spoon.
Place the shepherd's pie on a baking sheet to catch any spill over from the juices and cook until the yams are golden brown and the gravy is bubbling, around 25 minutes. Remove from oven and let cool 15 minutes before serving.