In a large heavy-bottomed pot like a Dutch oven, melt the butter over medium-high heat.

Add diced onion, carrots, and celery, cooking for about 5 minutes until they begin to soften.

Stir in the minced garlic and let it cook for an additional minute.

Sprinkle in the flour, stirring constantly for about a minute until there's a slight thickness.

Gradually pour in the evaporated milk and chicken stock, stirring to create a smooth roux. If you're using raw chicken, add the additional cup of chicken broth and the chicken pieces now.

Simmer for 20 minutes (or until the chicken is cooked through if using raw), then shred the chicken and return it to the pot. If using pre-cooked chicken, simply stir it in and keep the pot at a low boil.

Prepare the dumplings according to package instructions or your own preferred method.

Combine the flour, baking powder, salt, and thyme in one bowl.

In another bowl, stir together the milk and melted butter, then combine the wet and dry ingredients until just mixed.

Drop spoonfuls of the batter over the simmering chicken and broth, cover, and let steam for about 15 minutes.