Melt butter in a large stockpot or Dutch oven over medium heat. Add onion, carrots and celery. Cook, stirring occasionally, until tender, about 3-4 minutes. Stir in garlic and thyme until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Stir in wine, scraping any browned bits from the bottom of the stockpot.
Stir in chicken stock and half and half. Bring to a boil; reduce heat and simmer, stirring occasionally, until thickened, about 6-8 minutes.
Stir in chicken, peas and parsley; season with salt and pepper, to taste. Top with biscuits.
Place into oven and bake until bubbly and biscuits are heated through, about 8-10 minutes.
Serve immediately.
Notes
*Additional chicken stock can be used for white wine as a non-alcoholic substitute.