Bring the steaks to room temperature (about 30 minutes). Preheat the oven to 350 degrees F.

When the steaks are at room temperature, start heating a cast iron skillet over medium high heat. Don't use a non-stick pan as the high temperature you need to get it to will cause it to release toxic fumes. Generously salt and pepper both sides of the steaks and press the salt and pepper into the surface of the steaks to ensure it sticks.

When the skillet is very hot, place the steaks in the pan and allow them to brown undisturbed until they don't stick to the pan anymore. Flip and brown for another few minutes on the other side.

Quickly put the pan in the hot oven and turn it off. Allow them to rest in the oven without opening it for 10 minutes for a rare steak, or 15 minutes for medium rare steak.

Transfer the steaks to a plate, then return the skillet to the stove over medium heat. Add a splash of olive oil and saute the minced shallots until they start getting soft. Add the mushrooms and continue to saute until they are limp and glossy and there is no liquid in the pan.

Add the cognac and swirl it around the bottom of the pan to deglaze. Add the chicken stock and raise the heat to high, boiling until it starts to thicken and there's only about ¼ C of liquid remaining. Push the mushrooms and shallots to the back half of the pan, then add the butter to the other half. Whisk vigorously to incorporate, then stir it all together. Squeeze a splash of lemon juice in and whisk to combine.

Serve the mushrooms and sauce over the steak.