Place the chicken thighs, butternut squash, onion, garlic, chicken broth, sage, salt, and pepper into the slow cooker. Stir to combine the ingredients evenly.
Cover and cook on low for 6 hours until the chicken is tender and the squash is soft.
Remove the chicken thighs, shred them with two forks, and return the meat to the slow cooker. Stir to mix everything together.
In a mixing bowl, combine the flour, baking powder, milk, and melted butter to form a thick dumpling batter.
Drop spoonfuls of the batter onto the surface of the hot mixture in the slow cooker. Cover and cook on high for 1 hour until the dumplings are cooked through and no longer doughy in the center.