Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Season the chicken breast evenly with half of the sea salt, black pepper, and garlic powder.
Heat the olive oil in a skillet over medium-high heat and sear the chicken for 6 to 7 minutes per side until fully cooked and golden.
In a small bowl, combine the shredded parmesan cheese with the remaining garlic powder and dried oregano.
Spoon the cheese mixture onto the prepared baking sheet in small mounds, spacing them 2 inches apart.
Lightly flatten each mound with the back of a spoon and bake for 3 to 5 minutes until the edges are golden brown and crisp.
Remove the crisps from the oven and let them cool on the pan for at least 2 minutes to allow them to harden.
Toss the arugula with lemon juice and the remaining salt and pepper in a serving bowl.
Slice the cooked chicken breast and arrange it over the arugula, then top with the garlic herb parmesan crisps.