Place a large pot over medium heat and melt the butter.

Add the onion, carrots, and celery. Cook for about 5 to 7 minutes until the onions are translucent and the vegetables begin to soften.

Stir in the minced garlic and cook for just one minute until it smells fragrant.

Sprinkle the flour over the vegetables. Stir constantly for 2 minutes to cook out the raw flour taste, creating a thick paste.

Slowly pour in the chicken broth, one cup at a time, whisking or stirring well after each addition to eliminate lumps.

Add the diced chicken, potatoes, thyme, and rosemary. Season with a pinch of salt and pepper.

Bring the soup to a gentle boil, then turn the heat down to low. Cover the pot and simmer for 15 to 20 minutes, or until the potatoes are soft and the chicken is fully cooked.

Stir in the milk or heavy cream and the frozen peas. Let the soup cook for another 5 minutes until the peas are heated through and the soup has thickened.

Taste the soup and add more salt or pepper if needed. Garnish with fresh parsley before serving.