Bake the sweet potatoes: Place the sweet potatoes in a single layer on a baking sheet. Put the baking sheet in the center of the oven and bake until the potatoes completely yield when pierced with the tip of a knife, 1 to 1 1/2 hours.
For the meat: In a medium skillet, heat the oil over medium-high heat until smoking lightly. Add the ground turkey in small pieces and cook until browned and cooked through, 4 to 5 minutes. Season generously with salt and pepper. Transfer the meat with a slotted spoon to a large bowl. Add the onions, carrot and celery to the skillet, then season with salt and pepper, and cook until the vegetables are translucent and tender, 5 to 7 minutes. Pour off any excess grease. Transfer the vegetables to the bowl with the meat. Stir in the peas, broth and vinegar. Taste for seasoning.
Make the brown butter for the sweet potatoes: In a medium saucepan, melt the butter completely over medium heat. Wait until it starts to simmer and turn golden brown, 3 to 5 minutes. Remove from the heat. Dip a pastry brush in the butter and grease the bottom and sides of a 2-quart oval or rectangular baking dish; set aside. Remove the butter from the heat and stir in the brown sugar, molasses, ginger and cinnamon. Set aside and keep warm.
Make the purée: Let the roasted potatoes cool until still hot but cool enough to handle. Place them on a flat surface and cut them in half. Use a large spoon to scoop out the flesh. Discard the skins and put the flesh in a food processor. Pulse until the flesh starts to break down, then add the brown butter mixture, milk, orange zest and salt and pepper to taste. Alternatively, run the potatoes through a food mill into a large bowl, then add the brown butter, milk, orange zest and salt and pepper to taste. Mix well.
Lower the oven to 375 degrees F.
Spoon all of the meat mixture into an even layer in the baking dish. Dollop the mashed sweet potatoes over the meat, then spread the potatoes into a layer.
Place the dish on a baking sheet in the center of the oven and bake until the center is hot when poked with the tip of a knife and the top is browned, 30 to 35 minutes.
