Season the chicken breast with half of the sea salt and black pepper.
Heat a non-stick skillet over medium heat and cook the chicken for 6 to 7 minutes per side until the internal temperature reaches 165 degrees Fahrenheit.
Bring a small pot of water to a boil, carefully lower the eggs in, and simmer for 7 minutes for a jammy yolk.
Immediately transfer eggs to an ice bath for 3 minutes, then peel and halve them.
In a large bowl, combine the mixed greens, halved cherry tomatoes, and sliced cucumbers.
Whisk together the olive oil, lemon juice, Dijon mustard, and remaining salt and pepper in a small jar to create the dressing.
Slice the chicken into thin strips and arrange on top of the greens along with the halved eggs and walnuts.
Drizzle the dressing over the salad just before serving.