Toast rice in a small skillet over medium heat, shaking pan frequently, until golden brown, about 10 minutes. Let cool slightly, then grind to a powder in a mortar and pestle or spice grinder.

In a bowl, combine vinegar, 2 tablespoons lime juice, fish sauce, and minced lemongrass, ginger, and shallot. Heat sugar in a covered small saucepan over medium-low until it melts, about 5 minutes. Remove lid; continue cooking, swirling pan, until sugar is deep amber. Remove from heat. Carefully add vinegar mixture (mixture will bubble and harden). Return to medium heat and cook, stirring, until sugar dissolves again. Remove from heat; stir in remaining 2 tablespoons lime juice and peppers. Let cool completely.

Heat 1/4 inch oil in skillet over medium. When it shimmers, add lemongrass rounds and cook, stirring occasionally with a fork, until golden, about 2 minutes. Transfer to a paper towel-lined plate and sprinkle with salt. Fry ginger matchsticks and 1/2 cup shallot rounds, in separate batches, in same manner.

Season shrimp with 1/2 teaspoon salt. Heat a large skillet over medium-high. Swirl in 2 tablespoons oil. Add remaining 1/4 cup shallot rounds; cook until soft and golden in places, 2 to 3 minutes. Add shrimp and cook, stirring frequently, until opaque, 2 to 3 minutes. Transfer to a bowl and toss with vinegar mixture and rice powder. Refrigerate at least 1 hour and up to 1 day. Stir in peanuts and sliced mint and basil. Spoon mixture into lettuce leaves with cucumber. Top with whole herbs, fried aromatics, and more peanuts; serve.