Heat olive oil in a large pot over medium heat. Add the celery, carrots, and onion and cook for about 3 minutes until slightly softened. Add the garlic and saute for 30 seconds. Stir in the butter and flour and whisk for 1 minute to form a smooth roux.

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

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

Stir in the evaporated milk and frozen peas. Let the soup simmer gently over low heat while you prepare the dumpling dough.

In a mixing bowl, whisk together the flour, baking powder, and salt. Make a well in the center and add the milk, sour cream, and melted butter. Stir until just combined — do not overmix. The dough should be slightly sticky.

Bring the soup to a gentle simmer. Drop teaspoon-sized portions of dumpling dough onto the surface. Cover the pot immediately and simmer on low for 12 to 15 minutes without lifting the lid.

Check one dumpling by cutting it open — it should be fluffy and fully cooked through. Shred the reserved chicken and return it to the pot. Stir gently, garnish with fresh parsley, and serve hot.