From whimsical +‎ -ly.

whimsically (comparative more whimsically, superlative most whimsically)

1. in a whimsical manner
   • 1904, Jack London, chapter 30, in The Sea-Wolf (Macmillan’s Standard Library), New York, N.Y.: Grosset & Dunlap, →OCLC:

     "Now don't say that this is what you get for bringing a woman along," she said. She smiled at me whimsically, gloriously, and I knew there was no need for forgiveness.

   • 1905, Edith Wharton, The House of Mirth, New York, N.Y.: Charles Scribner’s Sons, →OCLC:

     As they drew nearer she was whimsically struck by a kind of family likeness between Miss Van Osburgh and Percy Gryce.