In a large pot, heat some olive oil over medium heat and add carrots, celery, onions, and garlic. Saute for a few minutes and then add chicken broth, bay leaf, and basil. Bring to a boil and then reduce heat to a simmer. Cover and cook until carrots and celery are tender.
When carrots and celery are almost done, add chicken and chopped parsley. Add evaporated milk and remove bay leaf.
Increase heat to boiling and add dumpling dough by the small spoonful (they'll puff up). Cook until until dumplings are cooked through (they should appear moist but feel firm; this is after about 4-5 minutes). If you're using raw chicken, simply add it in when the soup originally comes to a simmer and cook until internal temp reaches 165 degrees.
One other thing--if you know you'll have leftovers, only add dumplings or noodles to what you know you'll eat immediately. The noodles/dumplings will soak up all the liquid in the soup when you store it as leftovers, so you'll have overly-mushy noodles and chicken with no broth if you don't. The other thing you can do is add all of the dumplings or all of the noodles, and then store the dumplings or noodles separately from the rest of the soup. That's easy to do with dumplings, not so much with noodles.