Take the steak out of the refrigerator 20 minutes before you are ready to cook it so that it can come to room temperature. This will help it cook more evenly.
In a small pot over high heat, add the broth and wine and simmer until reduced by half, about 10 minutes.
Heat oil in a cast iron skillet over medium-high heat until it is very hot. Season the steak with the grill seasoning and put it in the skillet. Cook about 3 minutes per side for medium-rare. Remove it from the pan, cover it with foil, and let it rest for 5 minutes while you finish the sauce.
Reduce the heat under the skillet to medium and add the shallots. Cook until they begin to soften, about 3 minutes. Add the reduced broth and wine mixture and cook until thickened, about for about 5 minutes. Stir in the butter and cook until the butter is melted and incorporated into the sauce. Taste and adjust the seasoning with salt and pepper, if needed.
Slice the steak against the grain into thin slices, arrange them on a serving platter and serve with the sauce on the side or poured over top.