Preheat your oven to 425°F (220°C) and line a large sheet pan with parchment paper for easy cleanup.
Slice the fingerling potatoes into halves lengthwise and place them in a small bowl; toss with 0.25 tablespoons of olive oil, half of the sea salt, and half of the black pepper.
Pat the chicken breast dry with a paper towel. In a small ramekin, mix the oregano, garlic powder, lemon zest, and the remaining salt and pepper.
Rub the chicken breast with 0.25 tablespoons of olive oil, then coat thoroughly with the herb and zest mixture.
Arrange the chicken and potatoes on the prepared sheet pan, ensuring the potatoes are cut-side down for maximum browning.
Roast in the oven for 15 minutes.
While the chicken roasts, toss the broccoli florets with the remaining 0.25 tablespoons of olive oil and the lemon juice.
Remove the pan from the oven, add the broccoli to the empty spaces, and return to the oven for an additional 10 to 12 minutes until the chicken reaches an internal temperature of 165°F and the potatoes are golden.
Allow the chicken to rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted vegetables.