Preheat oven to 350 degrees F (175 degrees C). Line baking sheets with parchment paper.
Beat butter and sugar together in a large bowl with an electric mixer until smooth. Beat eggs into butter mixture one at a time; add vanilla extract and almond extract and mix until smooth.
Whisk flour, cocoa powder, pudding mix, baking soda, and salt together in a bowl. Stir 1/3 the flour mixture into butter mixture. Repeat with remaining flour mixture, mixing well after each addition. Fold cherries, chocolate chips, and chocolate chunks into dough. Drop cookie dough by the spoonful 2-inches apart onto the prepared baking sheets.
Bake in the preheated oven until golden and set, 10 to 15 minutes.