Season the chicken breast evenly with sea salt, black pepper, and half of the dried oregano.
Heat a grill pan or outdoor grill over medium-high heat until hot.
Grill the chicken for 6-7 minutes per side or until the internal temperature reaches 165 degrees Fahrenheit, then set aside to rest for 5 minutes.
Slice the halloumi into quarter-inch thick rectangles and grill for 1-2 minutes per side until golden brown grill marks appear.
In a small bowl, whisk together the lemon juice, lemon zest, extra virgin olive oil, and the remaining dried oregano to create the dressing.
Dice the cucumber and halve the cherry tomatoes.
In a large bowl, toss the mixed greens, cucumber, and tomatoes with the prepared lemon vinaigrette.
Slice the rested chicken and arrange it over the salad along with the warm, grilled halloumi slices.