Remove the steaks from the fridge about 30 minutes before cooking. Rub all over with olive oil. Season both sides with salt and pepper. Let steaks rest at room temperature for 30 minutes.

Preheat the oven to 400 degrees F (204 degrees C). At the same time, preheat a cast iron grill pan (or a cast iron skillet) on the stovetop over medium-high heat, about 3 minutes.

Once the oven is just a few minutes away from being preheated, add the butter and heat until melted. Add the steaks in a single layer. Sear for about 2 minutes, without moving around, until browned with grill marks on the bottom. Flip and sear for 1-2 minutes on the other side.

Transfer the pan to the preheated oven. Bake for 2 to 6 minutes, to your desired level of doneness.Use a probe thermometer to check internal temperature for best results, but a regular meat thermometer will work as well. These times are estimates for a 1.5-inch (~4 cm) thick steak:* 120 degrees F (49 degrees C), 1-2 minutes, for Rare* 130 degrees F (54 degrees C), 2-3 minutes, for Medium Rare* 140 degrees F (60 degrees C), 3-5 minutes, for Medium* 150 degrees F (66 degrees C), 4-7 minutes, for Medium Well* 160 degrees F (71 degrees C), 5-8 minutes, for Well DoneSteak temperature will increase by an additional 5 degrees when resting in the next step.

Remove the New York strip steaks from the oven, transfer to a plate or cutting board, and tent with foil. (Do not leave in the pan or they will be overcooked.) Let the steaks rest for 5 minutes before slicing.