Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Trim the ends of the Brussels sprouts and cut them in half lengthwise.
Place the sprouts on the baking sheet and toss with olive oil, sea salt, and black pepper until well coated.
Arrange the sprouts cut-side down and roast for 20-25 minutes until the outer leaves are crispy and charred.
While the sprouts roast, dice the chicken breast into bite-sized pieces and season lightly.
Heat a non-stick skillet over medium-high heat and sear the chicken until golden and cooked through, about 6-8 minutes.
Tear the prosciutto into small strips and add them to the skillet with the chicken for the last 2 minutes of cooking until crisp.
Remove the roasted sprouts from the oven and transfer them to the skillet with the chicken and prosciutto.
Drizzle the balsamic glaze over the mixture and toss everything together over low heat for 1 minute to marry the flavors.
Serve immediately while the sprouts are hot and the glaze is glossy.