In a small bowl, combine the mayo, lemon zest, and minced basil. Set aside.
Add olive oil to a preheated cast iron skillet over medium-high meat.
Blot the steak with a paper towel. Season both sides with salt.
Add steak to the hot skillet and leave it to cook for six minutes, untouched. This will allow the steak to get a good sear.
After six minutes, flip the steak and top generously with freshly ground black pepper. Cook for 5-6 minutes for medium rare, or a couple minutes longer for medium.
Once cooked, move steak to a plate and cover with aluminum foil. Let rest for five minutes.
While the steak is resting, prep your rolls with the other ingredients!
After resting, slice the steak and add it to the rolls. Delicious sandwiches assembled.