Heat a frying pan over medium heat, or set grill to 400 degrees. Slice the Halloumi lengthwise and place directly in pan or on grill. Cook until browned, then flip and cook until both sides are browned. Remove from pan or grill and set aside.

Toss the bread cubes in olive oil until lightly coated. Season generously with salt and pepper. Add to the pan and cook until golden brown and toasted, tossing frequently. Remove from pan and set aside.

Make the dressing: Whisk vinegar and mustard together. Whisking constantly, slowing pour in the oil until well combined. Whisk in the oregano.

Arrange lettuce among 4 dinner plates. Add remaining ingredients and pour dressing over top.