Prep the tilapia: Pat the fillets dry with paper towels.
Dry fish sears better and won’t stick as much.
Season the fish: In a small bowl, mix olive oil, minced garlic, paprika, oregano, 1 teaspoon salt, and 1/4 teaspoon pepper. Add lemon zest from half a lemon and 1 tablespoon of lemon juice. Brush or rub the mixture on both sides of the fillets.
Let sit for 10–15 minutes.
Set up your grill or pan: Preheat an outdoor grill to medium-high, or heat a grill pan or large nonstick skillet over medium-high heat. Lightly oil the grates or pan to minimize sticking.
Prep the broccoli: While the fish rests, cut the broccoli into even florets. Rinse and shake dry.
If you like tender stems, peel the thick stalks and slice them.
Steam the broccoli: Add an inch of water to a pot fitted with a steamer basket. Bring to a simmer, add the broccoli, cover, and steam for 4–5 minutes until bright green and just tender. Remove from heat and toss with a drizzle of olive oil, a squeeze of lemon, a pinch of salt, and pepper.
Add red pepper flakes if you like heat.
Grill the tilapia: Place the fillets on the hot grill or pan. Cook for 3–4 minutes on the first side without moving them. Flip carefully and cook another 2–3 minutes, until the fish flakes easily and is opaque throughout.
Finish with lemon: Transfer the tilapia to plates.
Squeeze fresh lemon over the top. Add a thin pat of butter to melt over the hot fish if you want a richer finish.
Plate and garnish: Serve the tilapia alongside the steamed broccoli. Sprinkle with chopped parsley and more lemon zest if you want extra aroma.
Check seasoning: Taste a bite of fish and broccoli.
Add a final pinch of salt, pepper, or lemon to balance everything.