Preheat your oven to 400°F (200°C).
On a large baking sheet, toss the broccoli florets with half of the olive oil and a pinch of the salt and pepper.
Roast the broccoli for 15-20 minutes until the edges are slightly charred and the stems are tender.
While the broccoli roasts, season the chicken breast on both sides with the dried oregano and the remaining salt and pepper.
Heat the remaining olive oil in a medium skillet over medium-high heat.
Place the chicken in the skillet and sear for 6-7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
Remove the chicken from the pan and let it rest for 3 minutes before slicing.
In the same skillet, reduce heat to low and add the minced garlic, lemon juice, and lemon zest, stirring for 30 seconds to pick up the browned bits from the pan.
Plate the sliced chicken alongside the roasted broccoli, drizzle with the lemon-garlic pan sauce, and finish with a sprinkle of grated parmesan.