Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Peel the carrots and slice them into half-inch thick rounds.
Season the chicken breast evenly with half of the sea salt, black pepper, and dried oregano.
In a medium bowl, toss the carrots with 0.5 tablespoons of olive oil, the honey, and the remaining salt and pepper.
Place the seasoned chicken and the glazed carrots onto the prepared baking sheet in a single layer.
Roast for 20 to 25 minutes until the chicken reaches an internal temperature of 165°F and the carrots are tender and browned.
While roasting, whisk together the remaining 0.5 tablespoons of olive oil, lemon juice, and finely chopped fresh parsley.
Remove the chicken from the oven and let it rest for 5 minutes before slicing it into thin strips.
Place the arugula in a large serving bowl and toss with the lemon-herb vinaigrette until lightly coated.
Top the dressed greens with the warm roasted carrots and the sliced chicken breast to serve.