Make mashed potatoes: In a large pot over high heat, cover potatoes with water and add a generous pinch of salt. Bring to a boil and cook until completely tender, 16 to 18 minutes. Drain and return to pot.
Use a potato masher to mash potatoes until smooth. Add melted butter, milk, and sour cream. Mash together until fully incorporated, then season with salt and pepper and fold in 1 cup cheese. Set aside.
Make turkey mixture: In a large, ovenproof skillet over medium heat, heat oil. Add onion, carrots, parsnips, garlic, thyme, sage and cook until fragrant and softened, 5 minutes. Deglaze with wine and cook 2 minutes more. Add ground turkey and cook until no longer pink, 5 minutes more.
Sprinkle meat with flour and stir to evenly distribute. Cook 1 minute more and add turkey broth. Bring to a simmer and let mixture thicken slightly, 5 minutes.
Top beef mixture with an even layer of mashed potatoes, sprinkle with remaining cheese and bake until there is very little liquid visible and mashed potatoes are golden, about 35 minutes. Broil if desired and garnish with parsley before serving.