Season the chicken breast with half of the sea salt and half of the black pepper.
Heat a grill or grill pan over medium-high heat and cook the chicken for 6 to 8 minutes per side until the internal temperature reaches 165°F.
While the chicken cooks, prepare the dressing by whisking together the extra virgin olive oil, fresh lemon juice, dried oregano, and the remaining salt and pepper in a small bowl.
Slice the cucumber into thin half-moons, halve the cherry tomatoes, and thinly slice the radishes.
In a large serving bowl, combine the mixed baby greens, sliced cucumber, cherry tomatoes, and radishes.
Drizzle the lemon-herb vinaigrette over the vegetables and toss thoroughly to ensure all the greens are lightly coated.
Remove the chicken from the heat, let it rest for 3 minutes to keep it juicy, then slice it into thin strips.
Top the salad with the grilled chicken strips, crumbled feta cheese, and pumpkin seeds for a final layer of texture and serve immediately.