Add the potatoes to a medium saucepan, cover with chicken broth and season with 1 teaspoon salt. Place over high heat and bring to a boil. Cover partially with a lid and cook, stirring occasionally, until the potatoes are fork-tender, around 12 minutes. Drain the cooking liquid into a large measuring pitcher and reserve.

Return the potatoes back to the pot and set the heat to the lowest setting. Add the butter and mash with a potato masher until incorporated. Add the milk, Greek yogurt (if using), ¼ teaspoon salt and ¼ teaspoon pepper. Mash with a potato masher until smooth. Taste the potatoes for seasoning and adjust with salt and pepper as desired. Cover with a lid and set aside until ready to use.

Preheat the oven to 450F.

Preheat a 10” oven-safe frying pan over medium-high heat. Add the olive oil and butter and heat until the butter has melted. Add the carrot, celery and onion, season with ¼ teaspoon salt and cook, stirring, until the onions are just translucent, around 4 minutes. Add the arrowroot starch and cook, stirring, until dissolved. Add the bone broth, milk, mustard, thyme and ½ teaspoon black pepper, bring to a simmer and cook, stirring regularly, until the liquid can coat the back of a spoon and has reduced in volume by ¼, around 10 minutes. Add the turkey and peas and stir through to combine. Taste the mixture for seasoning and adjust with salt and pepper, as desired.

Remove the pan from the heat and let it cool for 10 minutes so that the mixture can set. Using a spatula, carefully spread the mashed potatoes across the top of the turkey mixture. For extra texture, create small peaks and valleys in the potatoes with the back of a spoon. Place the pan on top of a large sheet pan to catch any drippings and transfer it to the oven. Bake the pie until the potatoes are golden brown and the filling is bubbling around the edges, around 20 minutes.

Remove the pan from the oven and let it cool at least 10 minutes before serving.