Heat a medium sauté pan over high heat. Season the quail with salt and pepper and add the butter to the pan, followed by the quail, breast side down. Cook the quail, without moving them, for about 4-5 minutes, then carefully flip the quail and baste very well with melted butter, spooning the butter over the breasts. Cook the second side for an additional 4-5 minutes, or until the quail is firm and tender. Once cooked, add the thyme to the pan and let it sizzle. Baste the quail with the thyme-scented butter a few times and remove from the pan to a plate, pouring the drippings over the quail. Rest for 5-10 minutes, then serve.
