Preheat your oven to 400°F (200°C).
On a large baking sheet, toss the halved Brussels sprouts, sliced carrots, and red onion wedges with 0.5 tablespoon of olive oil, half the sea salt, half the black pepper, and all of the dried oregano.
Spread the vegetables in a single layer and roast for 20-25 minutes, or until they are tender and show caramelized edges.
While the vegetables roast, season the chicken breast on both sides with the remaining sea salt and black pepper.
Heat the remaining 0.5 tablespoon of olive oil in a cast-iron or stainless steel 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 to rest. Reduce heat to low, add the minced garlic for 30 seconds until fragrant, then whisk in the lemon juice to deglaze the pan.
Slice the chicken and serve alongside the roasted vegetables, drizzling the lemon-garlic pan sauce over the top before serving.