Heat olive oil in a large pot over medium heat. Add celery, carrots, and onion, cooking for 3 minutes until slightly softened. Add garlic and sauté for 30 seconds.

Stir in butter and flour, whisking for 1 minute to form a roux.

Gradually whisk in chicken broth and bouillon, scraping up any bits from the bottom. Add thyme, sage, rosemary, salt, and pepper. Stir well.

Add chicken to the pot and bring to a boil. Cover, reduce heat to low, and simmer for 10 minutes until chicken is cooked through. Remove chicken to a cutting board and set aside.

Stir in evaporated milk and peas. Let simmer gently while preparing the dumplings.

In a mixing bowl, combine flour, baking powder, and salt. Make a well in the center, then add milk, sour cream, and melted butter. Stir until just combined. Do not overmix.

Bring soup to a gentle simmer. Drop teaspoon-sized portions of dumpling dough onto the surface of the soup. Cover and simmer on low for 12 to 15 minutes.

Check one dumpling for doneness. It should be fluffy and cooked through. Shred the chicken and return it to the pot. Stir gently to combine.

Garnish with fresh parsley and serve warm.