Preheat oven to 350°F. Pat turkey breast dry and lightly coat with oil or softened butter. Season the breast with poultry seasoning, Kosher salt and coarse black pepper and place on a wire rack set on a rimmed baking sheet or on a parchment-lined baking sheet.
Roast to an internal temperature of 165°F and let rest. Raise oven temperature and cook potato tots to package directions. When tots are done, remove from oven and cover loosely with foil. Switch the oven to broil.
Meanwhile, melt butter in a skillet over medium-high heat. When butter foams, add mushrooms and brown then season with salt and pepper. Add onions, garlic and stir 3-4 minutes to soften. Add flour and combine, whisk in a little stock then add tomato paste and whisk to combine and loosen up the paste. Whisk in remaining stock and Worcestershire; thicken gravy to coat the back of a spoon.
Thinly slice turkey breast. Slice 4-6 half-inch slices of white bread, 1 slice per portion.
Toast bread on both sides under broiler.
Arrange a few slices of turkey on each piece of toast and top with a little gravy and cheese, tots and more gravy and cheese. Broil sandwiches to melt cheese.
Transfer open-faced sandwiches to plates and serve.