Arrange the bread slices next to one another on a flat work surface. Using a glass or an 1-inch round coo0kie cutter, cut out two (2) small rounds from each sandwich; discard trimmings.
Spread each bread circle with 1 tablespoon butter. Place a thin layer of sliced onions over the butter. Lightly season the onions with salt. This is a great place to use your Fleur de sel.
Assemble the sandwiches with remaining bread slices, pressing lightly to make them adhere.
Spread some of the mayonnaise around the outside rim of each sandwich round. Roll the rim of each sandwich in the chives or parsley to coat completely.
Serve immediately or cover and refrigerator for a few hours.
Making Sandwiches Ahead of Time - If you need to make tea sandwiches in advance and need to keep them from drying out, cover them loosely with a sheet of wax paper and then place a damp kitchen towel over the wax paper (never place a damp towel directly on top of the bread because the sandwiches will become soggy. Refrigerate until serving time. When ready to serve, remove from refrigerator. Uncover sandwiches only just before serving.
Makes 16 sandwich rounds.