In a blender, add your loosely chopped onion, celery, carrots and 1 1/2 cups of your chicken broth. Blend until completely smooth and no chunks are left. Set aside.
In your dutch oven add your butter and garlic, and melt completely. Then slowly add 1 tablespoon at a time of flour while constantly whisking to be sure the mixture doesn't become clumpy or burn.
Once all flour and butter are combined, slowly stir in your remaining chicken broth while whisking to keep the consistency smooth.
Now pour in your blender mixture of veggies, your evaporated milk, and stir to combine.
Bring to a boil and add your thyme, black pepper, salt, and chicken and give it another stir.
Begin dropping in your sliced biscuits one at a time in different spots of your boiling mixture. Once all biscuit pieces have been dropped in, cover and cook for 15 minutes.
Enjoy a delicious bowl of Chicken & Dumplings!