Dice the chicken breast into small, bite-sized cubes and set aside.
In a medium pot, melt the ghee over medium heat. Add the diced onion, carrots, and celery, sautéing until the vegetables begin to soften.
Add the chicken cubes to the pot and cook for 3-4 minutes until the outsides are lightly browned.
Pour in the chicken broth and add the dried thyme. Bring the mixture to a gentle boil, then reduce heat to a low simmer.
While the broth simmers, whisk together the whole wheat flour, baking powder, sea salt, and black pepper in a small bowl.
Stir in the almond milk slowly until a thick dough forms. Do not overmix.
Using a small spoon, drop rounded tablespoons of the dough into the simmering broth. Ensure they are spaced apart.
Cover the pot with a tight-fitting lid and simmer for 10-12 minutes without lifting the lid, allowing the dumplings to steam and fluff up.
Remove from heat, garnish with freshly chopped parsley, and serve warm.