Velvet the beef first. In a bowl, toss the 1½ pounds sliced beef with the 1 tablespoon cornstarch, 1 tablespoon soy sauce, and 1 teaspoon vegetable oil until every piece is coated. Let it sit for 20 minutes at room temperature. This is the step that gives you that silky, tender beef you get at restaurants, the cornstarch forms a light coating that protects the meat from the high heat and locks in the juices.
While the beef marinates, whisk together the 3 tablespoons soy sauce, 2 tablespoons oyster sauce, 1 tablespoon fish sauce, 1 tablespoon brown sugar, 1 teaspoon rice vinegar, and ¼ cup beef broth in a small bowl. Set it within arm's reach of the stove, because this dish moves fast once it starts.
Heat the 2 tablespoons vegetable oil in a large skillet or wok over high heat until it shimmers. High heat is the whole secret to this dish, so do not rush it, let the pan get properly hot. Add the velveted beef in a single layer and let it sear undisturbed for 1 minute before stirring. Cook for 2 to 3 minutes total, until browned but not fully cooked through, then push it to one side or scoop it out onto a plate.
Add the sliced red and yellow peppers and the sliced onion to the same pan. Stir fry for 2 minutes, until they are crisp tender and starting to char at the edges.
Add the 4 cloves minced garlic, 1 tablespoon grated ginger, and the Thai chilies. Stir for 30 seconds, just until fragrant, taking care not to burn the garlic.
Return the beef to the pan and pour in the sauce. Toss everything together and cook for 1 to 2 minutes, until the sauce thickens slightly and coats the beef and vegetables.
Turn off the heat and fold in the 1½ cups Thai basil leaves, stirring just until they wilt. They go in at the very end so they keep their color and that distinct peppery anise flavor, which dies if you cook it too long.
Serve over the 3 cups warm jasmine rice, topped with the ⅓ cup chopped peanuts and lime wedges.