Combine butter, sugar, and whipping cream in a medium saucepan. Bring to a boil, stirring constantly. Stir in flour and ground almonds; mix well. Remove from heat; stir in orange extract, vanilla, and sliced almonds.
Drop dough by teaspoonfuls 3 inches apart onto aluminum foil-lined cookie sheets. Bake at 350° for 8 to 10 minutes. Let cool completely on cookie sheets; peel off aluminum foil. Store cookies in airtight containers.