Bring water, lemon juice, and salt (if desired) to a boil in a medium saucepan over high heat. Stir in brown rice. Cover, reduce heat, and simmer 45 minutes or until water is absorbed. Remove from heat. Cool for 10 minutes. Stir in chopped basil and lemon zest.
In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Add shrimp; sauté until pink, about 4-5 minutes. Using a slotted spoon, transfer shrimp to plate; cover to keep warm.
To the same skillet, add remaining olive oil, pine nuts, garlic, and shallots. Cook until browned and fragrant, about 3 minutes. Add mushrooms and tomatoes; continue cooking until tomatoes begin to burst with juices, about 3 minutes.
Remove from heat and stir in capers, paprika, salt, and cooked shrimp. Place an equal amount of lemon basil brown rice in four shallow bowls and top each with shrimp mixture. Garnish with basil sprigs and lemon wedges.