Place the chicken pieces, diced tomatoes with their juices, chicken broth, tomato paste, minced garlic, dried basil, salt, and black pepper into the slow cooker. Stir to combine everything evenly.
Cover and cook on low for 6 hours or on high for 3 hours until the chicken is fully cooked and tender.
In a mixing bowl, stir together the flour, baking powder, and salt. Pour in the milk and melted butter, then mix gently just until a soft dough forms. Avoid overmixing.
Drop rounded spoonfuls of the dumpling dough directly onto the surface of the hot mixture in the slow cooker. Replace the lid and cook on high for 1 more hour until the dumplings are cooked through and no longer doughy in the center.
Turn off the heat and sprinkle the chopped fresh basil over the top before serving.