1. Combine 1/4 cup coconut milk, mango, and next 4 ingredients (through soy sauce) in a mini food processor; process until smooth. Combine mango mixture and remaining 1 cup coconut milk in a small saucepan over high heat; bring to a boil. Cook until reduced to 1 cup (about 10 minutes). Stir in lime juice.
2. Combine tilapia, 1/3 cup panko, and the next 8 ingredients (through eggs) in a large bowl; toss gently to combine. Using damp hands, shape mixture into 6 equal balls. Place remaining panko in a shallow dish. Coat balls in panko; gently press each ball into a (3-inch) patty.
3. Heat a large skillet over medium heat. Add butter and oil to pan; swirl to coat. Add patties; cook 4 minutes on each side or until browned. Serve with sauce and rice.