Grate the zucchini using a box grater and place it in a clean kitchen towel; squeeze firmly over the sink to remove as much moisture as possible.
Season the chicken breast on both sides with the sea salt, black pepper, and dried oregano.
Heat 0.5 tbsp of the olive oil in a large skillet over medium-high heat.
Place the chicken in the skillet and sear for 6 to 7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
Remove the chicken from the pan and let it rest on a cutting board for 5 minutes.
In the same skillet, add the remaining 0.25 tbsp of olive oil and the minced garlic, sautéing for 30 seconds until fragrant.
Add the squeezed grated zucchini to the pan, tossing frequently for 2 to 3 minutes until tender but still vibrant.
Stir in the lemon juice, lemon zest, and fresh parsley, then remove the pan from the heat.
Slice the rested chicken breast into strips and serve atop the bed of zucchini, finishing with a sprinkle of parmesan cheese.