Make the pickle: Heat the granulated sugar and 1/2 teaspoon salt with the rice vinegar and 1/3 cup water in a small saucepan over medium-high heat, stirring, until dissolved. Combine the cucumber, sauerkraut, cherries, onion and chile pepper in a bowl and pour the hot brine on top. Let cool completely. Cover and refrigerate until ready to serve, or up to 2 weeks.
Make the soup: Grind the garlic, ginger, coriander and turmeric with a mortar and pestle or in a mini food processor to make a paste. Stir in the red curry paste.
Cook the coconut milk in a medium saucepan over medium heat, stirring, 5 minutes. Stir in the curry paste mixture and simmer, stirring, 3 more minutes. Add the chicken stock, chicken strips and brown sugar and simmer until the chicken is cooked through, about 10 more minutes.
Meanwhile, bring a pot of water to a boil. Add the lo mein noodles and cook until al dente, about 6 minutes. Drain.
Stir the soy sauce, fish sauce and peanut butter into the soup; cook, stirring until smooth, 5 more minutes. Remove from the heat and add the lime juice. Divide the noodles among 4 large bowls, ladle in the soup and top with the pickle. Top with cilantro, basil and chopped peanuts.