Heat butter and thyme sprigs in a small skillet over medium heat, swirling occasionally, until butter is melted and starting to brown, 2–3 minutes. Season liver with salt and pepper. Increase heat to medium-high. Quickly cook liver (careful, it may splatter), basting constantly, until golden and crispy on both sides, 30–45 seconds (you want the inside to be pink, so don’t overcook). Transfer liver to toast, drizzle with some butter from skillet, and scatter thyme leaves over.