Heat a large nonstick skillet or wok over medium heat.
Cook peanuts until golden, 8–10 minutes; let cool.
Transfer to a food processor; pulse until ground.
Return skillet to medium-high heat. In a piece of aluminum foil, wrap shrimp paste into a flat package; cook, flipping once, until toasted and fragrant, 2–4 minutes.
Let cool, unwrap, and transfer to food processor.
Add sugar, garlic, and chili; purée into a paste.
Transfer paste to skillet and add coconut milk; cook over medium heat, stirring constantly, until mixture begins to separate, 5–7 minutes.
Stir in vinegar, salt, and 1⁄2 cup water; simmer until sauce is thickened, 2–3 minutes.
Set aside
Heat 2" oil in a saucepan until a deep-fry thermometer reads 350°. Working in batches, fry potatoes until golden and cooked through, 3–4 minutes. Using a slotted spoon, transfer to paper towels to drain.
Fry tofu until puffed and golden, about 2 minutes; drain on paper towels.
Bring a large pot of salted water to a boil; working in batches, cook spinach, beans, sprouts, carrots, and cabbage until just tender, 30 seconds to 1 minute for spinach, beans, and sprouts and 2–3 minutes for carrots and cabbage.
Using a slotted spoon, transfer vegetables to a bowl of ice water until chilled; drain, spread on paper towels to dry, and transfer to a large platter. Add potatoes and tofu,.
Top with reserved sauce, shrimp chips, and eggs.