In a large heavy bottomed pot, melt butter over medium-high heat. Add vegetables - onion, celery, carrots and garlic. Cook, stirring often until tender, about 6 to 8 minutes.

Add the shredded cooked chicken, chicken broth, evaporated milk, and can of cream of chicken and bring to a simmer. Season soup to taste with salt and pepper.

Cut the biscuits into quarters (each biscuit will be sliced into 4 equal pieces) and lightly toss them in flour.

Add the floured biscuits to the soup and lightly press them under the broth with a spoon or spatula. Place the lid on the pot and cook the dumplings for about 8 to 10 minutes. If they get stuck together, you can break apart the dumplings and press them back under the broth.

Test one of the biscuits to ensure they have cooked through and are not raw in the middle. Once the biscuits are cooked through, serve immediately!