In a saucepan, add the coconut oil, chopped garlic cloves and grated ginger. Cook for 1 minute and add the basmati rice. Stir. Cover with a cup of hot water and season with salt. Cover and cook over low heat for about 15 minutes.
Cut the broccoli into small pieces and place in boiling water for about 3 minutes. Drain.
In a frying pan, add the olive oil and shrimp. Cook for 1-2 minutes. Add the chopped garlic cloves and chili pepper and cook for another minute.
In the meantime, mix the teriyaki sauce with the cornstarch in a bowl and stir until dissolved. Add this sauce and the broccoli to the frying pan. Cook for another 2-3 minutes.
Serve the basmati rice with the shrimp. Finish with sesame seeds and chopped chives (optional).