In a food processor, add all of the ingredients for the sauce: the garlic, ginger, green onions, oyster sauce, soy sauce, fish sauce, lime juice, 1 Tablespoon vegetable oil, and brown sugar. Pulse until all of the ingredients are combined into a sauce. Set aside.
In a large wok or skillet, heat 2 tablespoons of vegetable oil over medium heat. Add the red and green peppers and the onions and sauté for 2 minutes, just until the vegetables are slightly softened.
Pour in the white wine and stir together, cooking for 1 more minute.
Add the shrimp and stir, sautéing until the shrimp are cooked, about 3 minutes.
Pour in the sauce mixture, and stir. Add the coconut milk, stir, and then add the Thai basil leaves. Turn off the heat, and stir until the ingredients are well mixed. Serve immediately.
Notes
Makes 2-4 servings. This recipe makes two large, hearty dinner servings, or three to four average dinner portions. Serve over rice. Sauce notes: this makes a flavorful, thin Thai sauce. If you want it to be thicker, you can omit the vegetable oil in the sauce, and feel free to add a little more oyster sauce if you want a richer, thicker sauce. Basil: If you can't find Thai basil you can use regular basil leaves, but I suggest giving regular basil leaves a rough chop before adding. Optional: top each serving with a fried egg, and serve with a lime wedge.Storage: Store in an airtight container in the refrigerator for up to three days.