Heat the oven to 425°F. Line a large rimmed metal baking sheet with parchment, or lightly oil it with some of the divided olive oil.

Bring a large pot of well-salted water to a boil. Add the Brussels sprouts and cook for 7–9 minutes, until just tender but not falling apart.

Drain the Brussels sprouts thoroughly and let them steam-dry for several minutes. Pat away any visible moisture before arranging them on the baking sheet.

Use the bottom of a glass, measuring cup, or small pan to press each sprout flat to about 1/2 inch thick. Leave space between the pieces so hot air can circulate.

Drizzle the smashed sprouts with about 2 tablespoons of olive oil and season with 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Turn or nudge the sprouts as needed so the oil reaches the exposed cut surfaces.

Roast for 15–18 minutes, preferably with the cut sides against the pan, until the bottoms are browned and the edges begin to crisp.

Scatter the torn prosciutto over and around the Brussels sprouts. Return the baking sheet to the oven for 5–8 minutes, until the prosciutto is crisp and the sprouts are deeply browned.

Sprinkle the Parmesan over the roasted sprouts and prosciutto. Roast for 1–2 minutes more, just until the cheese softens or lightly browns.

Finish with fresh lemon juice and serve immediately. Add a small drizzle of balsamic glaze if desired.