Combine first 3 ingredients in a bowl. Heat oil in a large skillet over medium-high heat. Add shrimp; cook 3 to 4 minutes or until pink, stirring occasionally. (Shrimp will not be cooked through.) Remove from skillet; set aside.
Add bell pepper, curry paste, and curry powder to skillet. Cook for 2 minutes, stirring constantly. Stir in coconut milk, soy sauce, and brown sugar. Cook for 3 minutes or until curry paste dissolves, stirring constantly.
Stir in shrimp; cook 2 minutes. Remove from heat. Stir in cilantro, and serve immediately in shallow bowls over hot cooked rice.