Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Peel and cube the beetroot into 1/2-inch pieces and mince the garlic cloves.
Toss the beetroot cubes on the baking sheet with half of the olive oil, the minced garlic, and a pinch of sea salt and black pepper.
Roast the beets for 25-30 minutes, or until they are tender and slightly caramelized around the edges.
While the beets roast, season the chicken breast with the remaining salt and pepper, then grill or pan-sear over medium heat until the internal temperature reaches 165°F.
Let the chicken rest for 5 minutes before slicing it into thin strips.
In a large mixing bowl, whisk together the remaining olive oil and the lemon juice to create a simple vinaigrette.
Add the arugula, roasted beets, and sliced chicken to the bowl, tossing gently to coat every leaf and morsel in the dressing.
Transfer the salad to a plate and garnish with crumbled feta cheese and freshly chopped parsley.