Melt the butter in a large pot over medium-high heat. Add the onions, carrots, and celery to the melted butter and cook for 5 minutes. Once the vegetables have softened, add the garlic and cook until fragrant.
Once fragrant, add the flour and stir to combine. Once combined, add the evaporated milk and chicken stock and stir, then bring to a boil. Once boiling, add in the chicken, thyme, and black pepper and salt. Allow the soup to simmer uncovered.
While the soup simmers, make the dumplings. Whisk together flour, baking powder, pepper, salt, and thyme in a large bowl. Create a well in the center of the mixture and pour the butter and milk into the center. Use a rubber spatula or your hands to mix until a dough ball forms.
Form the dough balls into two tablespoons worth and place directly into the simmering pot. Gently press them down into the soup so they are slightly covered. Cook for about 15 minutes or until the dumplings are cooked through. Once the dumplings are cooked through, serve immediately.