Halve eggplants lengthwise. Peel a strip of skin down length of each half. Sprinkle 1⁄4 cup salt over eggplant and allow to drain for 1 hour.
Purée hot pepper, red peppers, garlic, 1⁄2 tsp. salt, and vinegar in a food processor until smooth. Transfer to a saucepan and bring to a boil over high heat. Reduce heat to medium and cook until sauce has thickened into a paste, about 15 minutes. Remove from heat and set aside.
Heat 2 tbsp. oil in a large skillet over high heat. Brush salt off eggplant, then blot dry with paper towel. Working in batches and adding more oil as needed, fry eggplant until soft and golden brown, about 5 minutes per side. Drain on paper towel.
Press with the back of a spoon to make an indentation lengthwise down center of each eggplant. Spoon 1 tbsp. of the pepper paste into each indentation.
Layer eggplant in a serving dish and serve warm or at room temperature. Or, layer in a plastic container, cover surface of eggplant directly with plastic wrap, then cover with a lid and refrigerate; flavor improves after 2 days.