Thaw the shrimp according to package instructions. Remove tails and devein shrimp. Set aside and chop if preferred.
Heat the oil in a large skillet over medium-high heat until fragrant. Add garlic and cook for 1 minute, stirring frequently.
Add ginger and onion and cook for three minutes, stirring frequently.
Add curry paste and cook for a minute, stirring constantly.
Add coconut milk, vegetable broth or water, lime juice, salt, and pepper. Bring the mixture to a boil, then reduce to a simmer.
Add shrimp and cherry tomatoes and cook until heated through, about 1 - 2 minutes.
Meanwhile, cook brown rice according to directions.
Serve shrimp coconut curry over brown rice. Top with basil.