1. Preheat the oven to 350°. In a medium bowl, toss the pork with half of the garlic and 1 tablespoon of the soy sauce. Set aside to marinate at room temperature for 1 hour.
2. In a medium ovenproof skillet, heat 2 teaspoons of the peanut oil. Add the onion and cook over moderately high heat, stirring occasionally, until evenly browned, about 5 minutes. Transfer the skillet to the oven and cook, stirring occasionally, until the onion is dry and deep brown, about 25 minutes. Remove from the skillet and set aside.
3. In a medium bowl, whisk the water with the remaining garlic and the vinegar, lime juice, chopped mint, fish sauce, sugar, salt and crushed red pepper.
4. In a bowl, toss the turnips with 3 tablespoons of the dressing. In another bowl, toss the carrots with 3 tablespoons of the dressing.
5. In a large skillet, heat the remaining 1 teaspoon of peanut oil over high heat. Add the pork strips in an even layer and cook, without stirring, until browned on the bottom, about 2 minutes. Turn and cook until browned on the second side, about 2 minutes longer. Add the remaining 1 tablespoon of soy sauce to the skillet and stir to coat the meat. Transfer the meat to a plate and let cool.
6. In a bowl, toss the lettuce, cabbage, shredded mint and pork. Add the remaining dressing and any excess dressing from the turnips and carrots. Arrange the turnips and carrots on opposite sides of each plate and mound the pork salad in the center. Sprinkle the browned onion and chopped peanuts over all and serve.: