Sprinkle the steak with a generous amount of salt and pepper on both sides. Add the vegetable oil to a heavy bottomed or cast iron pan set over medium high heat. Once the pan is searing hot, set the steak in it and don’t move it. Let it sear until it develops a nice char, 3 to 4 minutes (for medium rare). Flip the steak and sear it on the other side; cook until it reaches your desired doneness (another 3 to 4 minutes for medium rare). If the steak is getting too charred and you’re still not at your desired doneness, you can place it in a 400 degree oven to finish it off.
Let the steak rest for 10 minutes on a cutting board while you prepare the salad. Slice the corn off each cob and heat it for a few minutes in the same pan the steak was in. Sprinkle it with salt and pepper and, with a slotted spoon, transfer it to a mixing bowl along with the cucumbers, mozzarella and basil and some more salt and pepper. Drizzle the salad with the olive oil and lime or lemon juice. Toss well to coat. Slice the steak thinly, against the grain, and divide between two plates. Serve the salad alongside the steak.