Beat first 3 ingredients at medium speed with an electric mixer 2 minutes. Add egg, whipping cream, and vanilla; beat well. Combine flour, soda, and salt. Add to peanut butter mixture; stir well. Stir in peanuts.
Roll dough into 3/4" balls. Press dough into miniature (1 3/4") muffin pans lined with paper cups. Bake at 350° for 12 minutes. Remove from oven; press a peanut butter cup into center of each cookie. Bake 2 more minutes. Remove from oven. Cool completely in pan on a wire rack.