In a large skillet, heat the oil over medium-high heat. Add the garlic and chiles and cook until aromatic, about 30 seconds. Add the steak and cook, stirring frequently, 2 minutes. Add the shallots and bell pepper and cook 1 minute. Add the fish sauce, sweet soy sauce, black soy sauce and chili paste. Bring the mixture to a low simmer and cook, stirring frequently, until the meat is cooked through and the vegetables are tender, about 3 minutes.
Remove the skillet from the heat and stir in the basil and mint until wilted. Serve over rice.
If you can't find sweet and black soy sauce, use 1/4 cup regular soy sauce mixed with 1/4 cup honey or sugar.