For the sandwich spread: chop basil and toss into a small mixing bowl. Add mayonnaise, 1/2 of the minced garlic, salt, and 1/4 teaspoon pepper.
For the meat spices: In another small bowl mix parsley, 2 teaspoons of lemon zest, the remaining garlic, and 1/2 teaspoon pepper. Press meat spices onto the steak. Drizzle skillet with oil and cook steaks for 9-11 minutes or until medium-rare, flipping half-way through. Remove and place onto a cutting board. Allow meat to rest for 5 minutes before slicing.
Preheat sandwich press. Add spread to 4 slices of flatbread. Thinly slice steaks and lay onto bread. Add 1-2 slices of tomato and a slice of cheese. Add second slice of bread to the top, and place into a sandwich press. Cook until bread crisps and cheese melts. Slice in half or quarters.