Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Trim the ends of the Brussels sprouts and cut them in half, then toss them in a bowl with half of the olive oil, half of the salt, and half of the pepper.
Spread the sprouts onto the baking sheet and lay the prosciutto slices in a single layer next to them.
Roast for 15 to 20 minutes, removing the prosciutto once it is crisp and the sprouts when they are tender and charred.
While the vegetables roast, season the chicken breast with garlic powder and the remaining salt and pepper.
Heat the remaining olive oil in a skillet over medium-high heat and sear the chicken for 6 to 7 minutes per side until fully cooked.
In a small saucepan, whisk the balsamic vinegar and honey over medium heat for 3 to 5 minutes until it reduces into a thick glaze.
Slice the chicken and serve it alongside the roasted sprouts, crumbling the crispy prosciutto over the top and finishing with the balsamic drizzle.