Combine the brown rice and water in a small saucepan. Bring to a boil, reduce heat to low and cook until all the water is absorbed, about 25 minutes.

Melt the butter with the olive oil in a skillet over medium heat; cook the garlic in the butter and oil until fragrant, 1 to 2 minutes. Pour in the wine and lemon juice; reduce heat to medium-low and simmer. Stir in the shrimp and cook until the shrimp turns pink, stirring regularly, 5 to 7 minutes. Sprinkle the parsley over the shrimp and cook another 2 minutes. Add the cornstarch to the liquid and stir until it thickens, about 1 minute more. Serve hot over the brown rice.