Preheat oven to 350 degrees F (175 degrees C). Line baking sheets with parchment paper.
Combine brown sugar, butter, shortening, and white sugar in a large bowl; beat with an electric mixer until creamy. Mix in egg, molasses, heavy cream, and vanilla extract.
Mix flour, oats, coconut flakes, baking powder, and salt together in a separate bowl. Add to the creamed mixture; mix until dough is just combined. Fold in jackfruit.
Drop small spoonfuls of dough 2 inches apart onto the prepared baking sheets.
Bake in the preheated oven until edges are golden, 10 to 12 minutes. Cool on the baking sheets for 5 minutes. Transfer to a wire rack to cool completely.
