Slice eggplant into ¾"x3" sticks. In a medium bowl, toss them with the salt and allow to sit while you are prepping the rest of your ingredients. Slice the tomatoes in a similar fashion, lengthwise.
Mix the sugar, soy sauce, hoisin and 2 tablespoons of water in a small bowl, set aside.
After about 20 minutes rinse the eggplant and pat dry.
Place a large non stick pan or wok over medium heat. Toast the peanuts for a few minutes before adding the oil, garlic, ginger and the chili, stir fry for about 30 seconds.
Add the Thai basil sprigs and the shallot. Stir fry for 30 seconds more. Turn the heat up to medium high. Add the eggplant and cook, stirring occasionally for 10-15 minutes. Once the eggplant is cooked through, add the tomatoes. Cook for another 5 minutes until the tomatoes are soft, but not mushy.
Pour in sauce mixture. Stir-fry for another 1-2 minutes until sauce thickens a bit. Garnish with scallions. Serve with rice if desired.