Heat 2 tablespoons vegetable oil in a large pot over medium heat. Add onion, garlic, and ginger; cook and stir until softened, about 5 minutes. Add tomato paste and cayenne pepper; cook, stirring constantly, until dark and fragrant, about 2 minutes. Stir in tomatoes, 3/4 cup water, salt, and pepper. Cover and simmer over medium-low heat.
Heat remaining 1 tablespoon vegetable oil in a separate pot. Season stew meat with salt and pepper. Cook in the hot oil until browned, 1 to 2 minutes per side.
Stir meat into the simmering tomato mixture. Add jasmine rice. Pour in enough water to cover the rice. Cover and cook over medium heat, stirring occasionally, until stew meat and rice are tender, about 30 minutes.