Preheat the oven to 375 degrees F (190 degrees C). Grease baking sheets. Whisk together flour, baking soda, and salt; set aside.

Beat unsalted butter, butter flavored shortening, white sugar, and brown sugar with an electric mixer in a large bowl until smooth. Add eggs one at a time; beat in vanilla extract and almond extract with last egg. Mix in flour mixture until just incorporated. Fold in cherries, walnuts, pecans, and chocolate chunks, mixing just enough to evenly combine. Drop by rounded spoonfuls onto the prepared cookie sheets.

Bake in the preheated oven until browned around the edges, 11 to 13 minutes. Cool on cookie sheet for 2 minutes; remove cookies to a wire rack to cool completely.