How to Make It
In a steamer basket set over simmering water, steam the potato until tender when pierced with a fork, about 18 minutes. Let cool slightly, then peel the potato and coarsely grate it.
Heat 1 teaspoon of the vegetable oil in a large nonstick skillet. Add the mushrooms and cook over high heat, stirring occasionally, until beginning to brown, about 4 minutes. Add the onion and garlic and cook, stirring, until translucent, about 3 minutes. Transfer to a bowl and let cool.
If using cubed turkey breast, pulse in a food processor until coarsely ground or mince by hand.
Add the ground turkey to the mushroom mixture with the potato, ham, milk, parsley, sage, thyme, salt, and pepper and mix well. Shape the mixture into eight 3-inch patties.
Heat the remaining 1 teaspoon vegetable oil in the large nonstick skillet. Add the patties and cook over moderately high heat, turning once, until well browned and cooked through, about 3 minutes per side. Transfer to plates and serve.