Melt 2 tablespoons of butter in a large heavy-bottomed Dutch oven or stockpot over medium heat. Add the diced yellow onion, sliced carrots, and celery. Cook for 6 to 8 minutes, stirring occasionally, until the vegetables begin to soften and the edges develop gentle golden caramelization.

Stir in the minced garlic, fresh thyme leaves, minced rosemary, sea salt, black pepper, and poultry seasoning. Cook for 60 seconds until fragrant, allowing the herb oils to bloom in the warm butter.

Add the remaining 2 tablespoons of butter to the pot and let it melt. Sprinkle the 1/3 cup of flour evenly over the sautéed vegetables. Stir constantly with a wooden spoon for 1 to 2 minutes to cook out the raw flour taste and form a golden paste that coats every vegetable piece.

Slowly stream in 1 cup of chicken broth while whisking vigorously to dissolve the roux without lumps. Once smooth, pour in the remaining 3 cups of broth.

Bring the soup to a gentle simmer over medium-high heat. Reduce the burner to medium-low and simmer uncovered for 8 to 10 minutes, stirring frequently, until the broth thickens into a rich, silky gravy consistency and the carrots are fork-tender.

Reduce the heat to low. Stir in the heavy cream, shredded chicken, and frozen sweet green peas. Simmer gently for 3 to 4 minutes until the chicken is heated through and the peas turn bright vibrant green. Taste and adjust seasoning with additional sea salt and cracked black pepper if desired.

Ladle the steaming, creamy soup into shallow ceramic bowls. Sprinkle generously with freshly chopped parsley and extra cracked pepper. Crown each bowl with a warm, split golden flaky buttermilk biscuit and serve immediately!