Melt the butter in a large Dutch oven or pot over medium heat.
Whisk in the flour and cook for 1 to 2 minutes to create a smooth roux.
Gradually pour in the chicken broth while constantly whisking to prevent lumps.
Add the diced chicken, potatoes, carrots, thyme, and black pepper to the pot.
Bring the mixture to a gentle boil, then reduce the heat to low, cover, and simmer for 15 to 20 minutes until the vegetables are tender and the chicken is fully cooked.
Stir in the frozen peas, frozen corn, and heavy cream. Simmer uncovered for an additional 5 minutes until the soup thickens and the vegetables are heated through.
Stir in the fresh parsley, ladle into bowls, and serve hot with baked biscuits on top or on the side.