In a heavy skillet bring oil and the butter to a sizzle. Add the steaks and cook over medium heat, 8 minutes on each side for medium. Remove the steaks from the pan and cover to keep warm.
Add the shallots and the thyme to the pan; stir and cook for 1 minute.
Pour the vinegar and the wine: simmer for 2-3 more minutes.
Season with salt and pepper.
Add the butter and swirl until melted and well incorporate with the sauce.
Slice the steaks crosswise and pour the sauce over the steaks.