Sauté Veggies: Heat a large pot over medium heat. Add oil. Once hot, add celery, carrots and onion and sauté for 3 minutes. Add garlic and sauté for 30 seconds. Add butter and flour and whisk well for 1 minute.
Add Broth and Seasonings: Gradually stir in the chicken broth and bouillon, scraping up anything stuck to the bottom of the pot. Add thyme, sage, rosemary, salt and pepper.
Add chicken and bring mixture to a boil. Cover the pot with a lid, reduce heat and simmer for 10 minutes, or until chicken is cooked through. Remove chicken to a cutting board and rest for 5 minutes before chopping or shredding into small pieces. Return chicken to the pot and add evaporated milk and peas.
Make Dumplings: Combine flour, baking powder, and salt in a bowl. Make a well in the center and add milk, sour cream and melted butter. Stir until combined, but don’t over mix.
Add Dumplings: Bring soup to a simmer and then use a small spoon to drop teaspoon-sized amounts of dough all over the top of the simmering soup (the dumplings will double in size as they cook).
Cover the pot and simmer on low for 12-15 minutes. Remove lid, gently stir to break dumplings apart, and scoop out a dumpling to check for doneness. If still doughy, cover and cook for a few more minutes, until tender. Taste and adjust seasonings if desired.
Serve warm, with a sprinkle of fresh chopped parsley on top.
Notes
Use a wider pot / dutch oven when cooking to help keep the dumplings in a single layer. And using a mix of thigh and breast meat is good.