Preheat the oven to 375 degrees F (190 degrees C).
Combine butter, white sugar, brown sugar, eggs, vanilla extract, and almond extract in a large mixing bowl; beat with an electric mixer on medium speed until thoroughly mixed.
Combine flour and baking soda in a separate bowl; gradually add to the butter mixture, mixing until incorporated. Stir in white chocolate chips, cherries, and almonds. Drop teaspoonfuls of dough onto ungreased baking sheets.
Bake in the preheated oven until golden brown, 12 to 15 minutes.