In a shallow dish, combine 1 tablespoon olive oil, lemon juice, minced garlic, dried oregano, 0.5 teaspoon salt, and black pepper.
Place chicken breasts in the marinade and coat thoroughly; let sit for 15 minutes at room temperature.
Preheat a grill or cast-iron grill pan over medium-high heat (approximately 400°F/200°C).
Grill the chicken for 6 to 8 minutes per side, or until the internal temperature reaches 165°F (74°C).
Transfer chicken to a cutting board and allow to rest for 5 minutes before slicing into 0.5-inch strips.
In a small bowl, whisk together the remaining 2 tablespoons olive oil, balsamic vinegar, Dijon mustard, honey, and remaining 0.5 teaspoon salt to create the dressing.
In a large mixing bowl, toss the mixed greens, cherry tomatoes, cucumber, and red onion with half of the dressing.
Divide the salad base among four plates; top with sliced chicken, diced avocado, and crumbled feta.
Drizzle the remaining dressing over the assembled salads and serve immediately.