Put potatoes in a 2- to 3-quart pan and cover with about 1 inch of water. Bring just to a simmer over high heat, then cover, reduce heat to low, and cook, without letting water bubble, until potatoes are tender when pierced, about 50 minutes. Drain and immerse in cold water until lukewarm, about 5 minutes, or let stand at room temperature until warm, about 20 minutes. Cut crosswise into 1/4- to 1/2-inch-thick slices.
Meanwhile, in another 2- to 3-quart pan over high heat, bring about 1 quart water to a boil. Add green beans and cook until tender to bite, 3 to 6 minutes. Drain and immerse immediately in ice water until cool, about 2 minutes; drain again.
On dinner plates, arrange equal portions of potato slices, green beans, cucumber, jicama, carrot, eggs, chicken, watercress, and limes. Scatter crisp shallots equally over salads. Spoon gado gado dressing over salads and add salt and juice from limes to taste.
Crisp Shallots and Gado Gado Dressing: In an 8- to 10-inch frying pan, combine 3 tablespoons salad oil and 3/4 cup thinly sliced shallots. Stir frequently over high heat until shallots are well browned, 6 to 8 minutes; lift from pan with a slotted spoon and drain on paper towels. Add about 1/3 cup chopped fresh jalapeño chilies (with seeds for maximum heat), 1/2 teaspoon coriander seeds, and 1/2 teaspoon cumin seeds to pan; stir often until chilies are lightly browned, about 5 minutes. Scrape mixture into a food processor. Add about 2 tablespoons crisp shallots, 1 teaspoon grated lemon peel, 1 teaspoon anchovy paste, 1 tablespoon minced fresh ginger, 2 tablespoons soy sauce, 2 tablespoons packed brown sugar, 1/3 cup lime juice, and 2/3 cup chunky-style peanut butter; whirl until ingredients are well mixed. Add 1 cup canned coconut milk (reduced fat or regular; stir before using) and whirl until well blended. Use, or cover and chill up to 1 week. Makes 2 1/2 cups; allow 1/4 to 1/2 cup per serving.