Preheat oven to 400°F with rack in lower third position. Toss 8 cups broccoli, 3 tablespoons oil, 1 teaspoon Italian seasoning, ½ teaspoon pepper and ¼ teaspoon salt in a 9-by-13-inch metal baking pan (do not use a glass pan, which could shatter). Roast, stirring once halfway through, until browned in spots and mostly tender, 20 to 25 minutes.
Stir ⅓ cup broth, the grated garlic and 1 teaspoon lemon zest into the broccoli. Roast until the liquid has almost completely evaporated, about 5 minutes. Sprinkle with the remaining ⅛ teaspoon salt.
Transfer to a serving platter. Sprinkle with ¼ cup feta and drizzle with 1 tablespoon lemon juice.
