In a saucepan, cover the potatoes with cold water and bring to a boil over high heat. Reduce heat to medium, cover, and simmer for 20 minutes until tender when pierced with a skewer. Drain and let cool for 20 minutes.
For the peanut sauce, combine peanuts and chillies in a food processor until finely chopped. In a saucepan over medium heat, warm oil. Stir in garlic and ginger for 30 seconds until fragrant. Add coconut milk, soy sauce, lime or lemon juice, sugar, and peanut mixture. Stir well, bring to a simmer, then transfer to a heatproof serving bowl.
Blanch the asparagus and beans in salted boiling water for 2 minutes until vibrant green and al dente. Drain, then quickly cool under cold running water and drain thoroughly.
Quarter the potatoes lengthwise. Plate the potatoes, asparagus, beans, bean sprouts, cucumber, tofu, egg, and tomato. Serve promptly with the peanut sauce.