Preheat oven to 400 degrees F (200 C) and line 2 baking pans with foil. Spread the plums out on one of the pans and the carrots on the other pan and brush them with oil. Bake for about 30 minutes until the plums are very wrinkled and dark-looking and the carrots are browning on the edges. Remove and cool for about 5 minutes. (Note: please be careful with the juices when pulling the plum pan out, it could spill on you and it's hot--ask me how I know this [hehe, oops].
Heat 1 tablespoon oil in a medium sauce pan and combine onions, garlic, and about half of the roasted plums over medium heat. Cook for 5 to 6 minutes until onions are browned, smashing the plums as you stir. Pour in 1 cup water to deglaze the pan and then add all other ingredients and simmer over low heat until thickened. You can add extra water if sauce gets too thick. You should have about 3 cups.
Cool and pour any extra into sealable container and store in refrigerator. It should last for at least 3 weeks but I've kept it way longer before. You can also freeze.
Combine the ground chicken, panko, onion, garlic, salt and pepper in a large, preferably stainless steel, bowl and mix well with a large spoon or clean hands. Form mixture into balls, about 2 inches, and place them on a foil lined tray.
Heat 1 tablespoon of olive oil in a large skillet and add the meatballs and tomatoes. Cook for about 2 to 3 minutes on each side until browned. Reduce heat to low and add the chicken broth and bbq sauce. Cover and simmer for about 20 minutes until the sauce has thickened and meatballs are fully done.
Fill 4 to 6 bowls with desired amount of warm steamed rice. Top with meatballs and garnish the bowls with cucumbers, cabbage, and roasted carrots, and roasted plums.