Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Trim and halve the Brussels sprouts, then toss them on the baking sheet with olive oil, sea salt, black pepper, and garlic powder.
Roast the sprouts for 20-25 minutes, flipping halfway through, until they are tender and the edges are charred.
While sprouts roast, place prosciutto in a large skillet over medium heat and cook until crisp, then remove and crumble into shards.
Season the chicken breast and sear in the same skillet for 5-7 minutes per side until cooked through, then slice into strips.
In a small bowl, whisk the balsamic vinegar and honey, then toss with the roasted sprouts, chicken, and prosciutto before serving.