Preheat your oven to 400°F (200°C) and line a rimmed baking sheet with parchment paper.
Rinse the basmati rice in a fine-mesh sieve under cold water until the water runs clear to remove excess starch.
In a small saucepan, combine the rinsed rice, water, and half of the minced garlic; bring to a boil over medium-high heat.
Once boiling, reduce the heat to low, cover tightly, and simmer for 15 minutes until the water is absorbed.
While the rice cooks, pat the tilapia fillets completely dry with paper towels and place them on the prepared baking sheet.
In a small bowl, whisk together the extra virgin olive oil, lemon juice, remaining garlic, dried oregano, sea salt, and black pepper.
Brush the lemon-herb mixture generously over both sides of the tilapia fillets and arrange the broccoli florets around the fish.
Bake in the center of the oven for 12 to 15 minutes, or until the tilapia is opaque and flakes easily with a fork.
Remove the rice from the heat and let it stand covered for 5 minutes, then fluff with a fork and stir in the chopped fresh parsley.
Portion the garlic rice onto a plate and top with the baked tilapia fillets and roasted broccoli.