Dice the onion, carrots, and potato into small, even pieces. Cut the chicken into bite-sized pieces and mince the garlic so everything is ready before cooking.
Melt the butter in a large pot over medium heat. Add the onion and carrots and cook for 4 to 5 minutes until the onion softens.
Add the garlic and cook for about 30 seconds. Add the chicken, thyme, salt, and black pepper, then cook for 4 to 5 minutes until the outside of the chicken is no longer pink.
Sprinkle the flour over the chicken and vegetables and stir for about 1 minute to cook the flour and coat everything evenly.
Slowly pour in the chicken broth while stirring constantly to prevent lumps. Bring the soup to a gentle boil.
Add the diced potato, reduce the heat to medium-low, and simmer for about 15 minutes until the potatoes are tender.
Stir in the frozen peas and heavy cream and cook for another 5 minutes until the peas are tender and the cream is heated through.
Check that the chicken is fully cooked. Taste and adjust the salt, pepper, or thyme, and add extra broth if you want a thinner soup.
Turn off the heat and let the soup rest for a couple of minutes so the creamy broth can settle and thicken slightly.
Ladle the soup into bowls and serve warm with biscuits or crusty bread and optional fresh parsley.