Preheat your oven to 400°F (200°C).
On a large rimmed baking sheet, toss the broccoli florets with 0.5 tbsp of olive oil, 0.25 tsp of sea salt, and 0.125 tsp of black pepper.
Roast the broccoli for 15 to 20 minutes until the florets are tender and the edges are slightly charred.
While the broccoli roasts, season the chicken breast on both sides with the remaining sea salt, black pepper, and the dried oregano.
Heat the remaining 0.5 tbsp of olive oil in a large skillet over medium-high heat.
Place the chicken in the skillet and sear for 6 to 7 minutes per side, or until the exterior is golden brown and the internal temperature reaches 165°F.
In the final minute of cooking, add the minced garlic to the skillet and sauté for 30 to 60 seconds until fragrant.
Remove the skillet from the heat, then pour in the fresh lemon juice and lemon zest, tossing the chicken to coat it in the bright glaze.
Serve the lemon-herb chicken immediately alongside the roasted broccoli.