Place a large skillet over medium-high heat with 2 turns of the pan of vegetable oil, about 2 tablespoons.
In a large mixing bowl, combine the ground turkey with the sour cream, scallions, salt and ground black pepper.
Using your hand, score the meat into four, then form four thin patties about half an inch thick out of each portion, adding them to the hot pan as you shape them. Cook until golden brown and cooked through, about 6 minutes per side. When finished cooking, remove the patties from the pan and wipe the pan clean with a paper towel.
While the patties are cooking up, place 4 slices of bread on a clean work surface and butter one side of each piece. Return the pan that the patties were cooked in over medium heat and add in the remaining butter. Once melted, place the remaining unbuttered slices of bread in the pan, place one piece of cheese on each slice, a turkey patty, one more slice of cheese and cap each off with the four slices of buttered bread, butter side up.
Cook sandwiches in the pan until toasted and the cheese has melted, about 2 minutes per side.