Preheat your oven to 400°F (200°C) and preheat a grill or cast-iron grill pan over medium-high heat.
In a small mixing bowl, whisk together 0.5 tbsp of olive oil, the lemon juice, lemon zest, minced garlic, dried oregano, sea salt, and black pepper.
Place the chicken breast in a shallow dish and pour half of the lemon-herb marinade over it, turning to coat evenly; let it marinate for at least 10 minutes.
On a large rimmed baking sheet, toss the broccoli florets with the remaining 0.5 tbsp of olive oil and a small pinch of additional salt.
Spread the broccoli in a single layer and roast in the oven for 15-20 minutes until the edges are slightly charred and the stems are tender.
While the broccoli roasts, place the chicken on the hot grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F.
Remove the chicken from the grill and let it rest for 5 minutes to lock in the juices before slicing.
Plate the sliced chicken alongside the roasted broccoli and garnish with an extra squeeze of fresh lemon if desired.