For the herb butter, combine all the butter ingredients in a mixer fitted with a paddle attachment. Beat until mixed, but 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 herb butter. Place smoked salmon on 4 of the slices. Top with the other 4 slices of bread, butter side down. Place the sandwiches on a baking sheet and wrap with plastic. Refrigerate until the butter is very cold. Place the sandwiches on a cutting board. 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.
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