For the scallion cream cheese, combine the cream cheese, scallions and the salt and pepper in an electric mixer fitted with a paddle attachment. Do not whip.
For the sandwiches, have the store slice the bread lengthwise on a meat slicer into 1/4-inch-thick slices. (If that isn't possible, you can slice it crosswise with a very sharp knife.)
Lay out 8 slices of bread and spread them all with a thin layer of scallion cream cheese. Place a single layer of turkey on half the slices, cutting the edges to fit the bread. Place the basil leaves randomly on top of the turkey. Top with the other 4 slices of bread, cream cheese side down. Lay the sandwiches on a baking sheet covered with parchment paper, cover with damp paper towels and wrap the sheet with plastic. Refrigerate until the cream cheese is cold and firm. Place the sandwiches on a cutting board and, with a very sharp knife, cut off the crusts. Cut each large sandwich in half crosswise, and then cut each half diagonally, twice, to make a total of 8 small triangles. (If the bread was cut crosswise, follow the assembly directions, then cut off the crusts and cut diagonally, twice, to make 4 small triangles.) Serve chilled.