Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Prepare the vegetables by slicing the carrot into thin rounds, chopping the broccoli into bite-sized florets, and cutting the bell pepper into strips.
Place the vegetables on the prepared baking sheet and toss with 0.5 tablespoon of olive oil, 0.25 teaspoon of sea salt, and 0.25 teaspoon of dried oregano.
Spread the vegetables in a single layer and roast for 20 to 22 minutes until they are tender and the edges are slightly caramelized.
While the vegetables roast, season the chicken breast evenly on both sides with the remaining salt, black pepper, garlic powder, and the rest of the oregano.
Heat the remaining 0.5 tablespoon of olive oil in a heavy-bottomed skillet over medium-high heat until shimmering.
Carefully place the chicken in the skillet and sear for 6 to 8 minutes per side, or until the exterior is golden brown and the internal temperature reaches 165°F.
Remove the chicken from the skillet and let it rest on a cutting board for 5 minutes to lock in the juices before serving alongside the roasted vegetables.