Prepare the vinaigrette by whisking together the olive oil, lemon juice, dried oregano, sea salt, and black pepper in a small bowl until emulsified.
In a large mixing bowl, combine the mixed salad greens, halved cherry tomatoes, sliced cucumber, and red onion.
Preheat a grill pan or heavy-bottomed non-stick skillet over medium-high heat.
Pat the halloumi slices dry with paper towels to ensure even browning.
Place the halloumi slices on the hot grill pan and cook for 2 minutes per side, or until golden-brown grill marks appear and the cheese is softened.
Toss the salad vegetables with two-thirds of the prepared vinaigrette and distribute evenly between two serving plates.
Arrange the warm grilled halloumi slices on top of the salad beds.
Drizzle the remaining vinaigrette over the cheese and serve immediately while the halloumi is warm.