Make the sauce. In a small bowl, whisk together the chili paste, soy sauce, fish sauce, brown sugar, and lime juice until incorporated. Set aside.
In a large skillet, heat the oil over medium-high heat. Once the oil is glistening, add the ground beef and cook, breaking the meat up with a wooden spoon, until browned, 8 to 10 minutes.
Add the bell pepper, onion, and garlic to the beef and cook until the vegetables start to soften, about 5 minutes.
Pour the sauce into the skillet. Add the fresh basil (reserving a fresh few leaves for garnish) and continue to cook, stirring, until the basil starts to wilt, about 2 minutes.
Serve the beef and basil over the rice, topped with the reserved basil leaves and cilantro, if using.