Heat a sauté pan to medium heat and add 3 tbsp vegetable oil. Add the shallots and cook until they are tender. About four minutes. Add the mushrooms and cook until they begin browning. About four minutes. Add the wine and cook until you stop smelling alcohol, then add stock and thyme leaves. Bring to a simmer and cook until mixture is reduced in half. Add salt and pepper to taste. Remove from heat.
Heat a heavy-bottomed pan to medium-high heat. Add 2 tbsp of oil. Season the hanger steak with salt and pepper. Place hanger steak into pan, and let sear for 4-5 minutes. Flip once and let other side cook until medium rare.
Remove steak from pan and let rest for five minutes. Slice into 1 inch pieces and top with sauce.