Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a medium bowl, toss the broccoli florets with 0.5 tablespoons of olive oil, half of the sea salt, and half of the black pepper.
Spread the broccoli in a single layer on the baking sheet and roast for 15-20 minutes until the edges are tender and slightly charred.
While the broccoli roasts, finely mince the garlic and chop the fresh cilantro.
In a small jar or bowl, whisk together the lime juice, cilantro, minced garlic, cumin, and the remaining 0.5 tablespoons of olive oil to create the dressing.
Season the chicken breast with the remaining salt and pepper.
Heat a non-stick skillet over medium-high heat and sear the chicken for 6-7 minutes per side, or until the internal temperature reaches 165°F.
During the last minute of cooking, pour the cilantro-lime dressing over the chicken in the skillet to glaze it.
Plate the zesty chicken alongside the roasted broccoli and drizzle any remaining pan juices over the top.