Melt butter in a large Dutch oven over medium heat. Sauté the onion, carrots, and celery for 6-7 minutes until softened, then stir in garlic, thyme, and poultry seasoning.
Sprinkle flour over the vegetables and stir constantly for 90 seconds. Slowly whisk in the chicken broth until smooth.
Add the cubed Yukon Gold potatoes, bring to a gentle boil, and simmer for 12-15 minutes until potatoes are fork-tender.
Reduce heat to low and stir in the shredded chicken, frozen peas, and heavy cream. Simmer 3-4 minutes until thick and heated through.
Ladle into warm bowls and serve topped with flaky buttermilk biscuits or puff pastry squares.