Preheat the oven to 425°F (220°C). Line a baking sheet with foil or parchment paper.
Toss the broccoli florets with 4 tablespoons olive oil and 1/2 teaspoon of the kosher salt, then spread in a single layer on the prepared baking sheet with flat sides down for best caramelization.
Roast the broccoli in the preheated oven for 15 minutes.
While the broccoli roasts, combine the shrimp, remaining 1 tablespoon olive oil, lemon zest, the remaining 1/2 teaspoon kosher salt, 1/2 teaspoon fresh ground pepper, and minced garlic in a medium bowl; toss to coat and let marinate for 10–15 minutes.
When the broccoli has roasted 15 minutes, add the marinated shrimp to the baking sheet and gently spread so everything is in a single layer.
Roast an additional 5 minutes, or until the shrimp are opaque and no longer translucent.
Remove from the oven, grate the fresh Parmesan over the shrimp and broccoli, and serve with lemon wedges.