Prep: Cut halloumi in half, hamburger style, to create 2 patties. Slice tomato into thick slabs. Sprinkle halloumi and tomato slices evenly with the oregano and pepper. Toast the hamburger buns.
Sauce: Mix together mayo and garlic.
Cook: Add a splash of oil or cooking spray to a large nonstick saute pan and set over high heat. Add halloumi and tomato slabs, cooking both sides until charred, about 5 minutes.
Assemble: Spread mayo sauce onto the bottom piece of both hamburger buns. Follow with a few pieces of lettuce, the halloumi, and the tomatoes. Serve hot!