Melt butter in a large heavy-bottomed pot over medium-high heat. Add diced onion, matchstick carrots, and celery. Cook for 5 minutes until they begin to soften, then add minced garlic and sauté for 1 more minute.

Stir in flour and combine completely, allowing it to cook for 1 minute while stirring constantly. Gradually pour in evaporated milk and chicken stock, mixing well to avoid lumps.

If using raw chicken: Add 1 cup more of chicken broth and the raw chicken to the pot. Simmer for 20 minutes or until the chicken is cooked through. Shred the chicken and return it to the soup for extra flavor.

If using pre-cooked chicken: Bring the mixture to a boil, then add the shredded chicken along with thyme, black pepper, and salt. Lower the heat, letting the soup simmer while you prepare the dumplings.

Whisk together the flour, baking powder, pepper, salt, and thyme for the dumplings in a medium bowl. Create a well in the center and pour in whole milk and melted butter.

Mix until a dough ball forms, being careful not to over-mix the batter. If the dough seems too dry, add an additional tablespoon of milk.

Scoop dough using a cookie scoop and drop it directly into the simmering soup, spacing them around the pot. Gently press each dumpling down so they are covered by the soup.

Reduce the heat to a low simmer and cover the pot with a lid. Let the dumplings cook for about 15 minutes, ensuring that the soup continues to simmer underneath.

Check for doneness by gently stirring the soup and cutting one dumpling in half. If it’s undercooked, allow it to simmer for an additional 3 to 4 minutes before serving.