Beat brown sugar, shortening, and eggs in a large bowl with an electric mixer until well combined. Mix in milk, vanilla, and almond extract. Add flour mixture gradually, beating well after each addition. Stir in cherries and chocolate chunks.
Place dough in the refrigerator for 1 hour.
Preheat the oven to 400 degrees F (200 degrees C).
Drop heaping tablespoons of dough 2 inches apart onto ungreased baking sheets.
Bake in the preheated oven until the edges are golden, 8 to 10 minutes, switching racks halfway through.