Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Place the broccoli florets on the baking sheet and toss with 0.5 tablespoons of olive oil, a pinch of the sea salt, and a pinch of black pepper.
Roast the broccoli in the oven for 18-20 minutes, or until the edges are crispy and the stems are tender.
While the broccoli roasts, prepare the zesty dressing by whisking together the lime juice, finely chopped cilantro, minced garlic, ground cumin, and 0.5 tablespoons of olive oil in a small bowl.
Season the chicken breast with the remaining sea salt and black pepper.
Heat the remaining 0.5 tablespoons of olive oil in a medium skillet over medium-high heat.
Add the chicken to the skillet and sear for 6-7 minutes per side, or until the internal temperature reaches 165°F.
Once cooked, remove the chicken from the heat and brush it generously with the cilantro-lime mixture.
Plate the chicken alongside the roasted broccoli and drizzle any remaining dressing over the vegetables before serving.