Strain pan drippings through a fine-mesh sieve; discard solids and reserve 2 1/2 cups pan drippings; set aside.
Melt butter in a medium saucepan over medium heat. Whisk in flour and thyme until lightly browned, about 1 minute.
Gradually whisk in reserved pan drippings. Bring to a boil; reduce heat and simmer, whisking constantly, until thickened, about 5-10 minutes. Stir in parsley; season with salt and pepper, to taste.