Place the chicken thighs in the slow cooker. Add the chicken broth, grated ginger, four sliced scallions, and soy sauce. Stir once to combine.
Cover and cook on low for 6 hours until the chicken is very tender.
Remove the chicken to a plate and shred it with two forks. Return the shredded chicken to the slow cooker.
In a bowl, stir together the flour, baking powder, and salt. Pour in the milk and melted butter and mix just until a soft dough forms.
Drop spoonfuls of the dough onto the surface of the simmering broth. Cover and cook on high for 30 minutes until the dumplings are cooked through.
Slice the remaining two scallions and scatter them over the finished dish before serving.