Preheat the oven to 425 degrees F. Meanwhile, toss the broccoli with 3 tablespoons olive oil and some salt and pepper. Place on a baking sheet.
Bake until the broccoli is cooked through and starting to brown, about 25 minutes.
Meanwhile, heat the remaining 1 tablespoon oil in a small skillet over medium heat. Add the garlic and sage and cook, stirring, until they are fragrant, 1 to 2 minutes. Transfer to a large bowl. When the broccoli is ready, add it to the bowl along with the Parmesan and lemon zest and juice, and gently toss. Transfer to a serving platter and serve immediately.