Rinse the quinoa thoroughly in a fine-mesh strainer and cook in 0.5 cup water according to package directions until all liquid is absorbed and quinoa is fluffy.
Season the chicken breast evenly on both sides with half of the sea salt, black pepper, and dried oregano.
Heat a skillet over medium heat with 0.5 tbsp of olive oil and sear the chicken until golden brown and cooked through, approximately 6 minutes per side.
While the chicken is cooking, dice the cucumber, halve the cherry tomatoes, and finely chop the fresh parsley.
In a small mixing bowl, whisk together the remaining 0.5 tbsp of olive oil, lemon juice, minced garlic, and the remaining spices to create the dressing.
Transfer the cooked quinoa to a large bowl and toss with the cucumber, tomatoes, parsley, and the prepared lemon-herb dressing.
Slice the warm chicken breast into strips and serve immediately over the quinoa salad.