Beat first 4 ingredients at medium speed with an electric mixer until blended. Spread evenly on 1 side of wheat bread slices. Spread 1 side of white bread slices evenly with Basil Butter. Press together spread sides of 1 wheat slice and 1 white slice. Repeat procedure with remaining bread slices.
Trim crusts from sandwiches. Cut sandwiches with a 2-inch round cutter. Roll sides in walnuts, if desired.