Cook the Potato & Eggs: Place the potato and eggs in a saucepan and cover with cold, salted water.
Bring to a boil.
Cook the potato for 10-15 minutes until tender.
After the water boils, turn off the heat, cover the pot, and let the eggs sit for 10-12 minutes.
Remove eggs and potato. Plunge eggs into an ice bath, then peel and quarter.
Let the potato cool slightly before dicing.
Blanch the Vegetables: Bring a separate large pot of salted water to a boil.
Add the green beans, carrots, cabbage, and cauliflower.
Cook for 2-4 minutes until tender-crisp.
Using a colander, immediately drain the vegetables and rinse with cold water to stop the cooking process.
Make the Peanut Sauce: In a small bowl, whisk the peanut butter with hot water until smooth.
In a saucepan, heat the vegetable oil over medium heat.
Sauté the minced garlic and shallots until fragrant, about 2-3 minutes.
Stir in the peanut butter mixture, salt, hot sauce, brown sugar, soy sauce, and lemon juice.
Cook, stirring constantly, until the sauce is smooth and slightly thickened. If it's too thick, add another tablespoon of hot water.
Assemble the Salad: Create a bed of lettuce leaves on a large serving platter or in individual bowls. Artfully arrange the diced potato, blanched vegetables, fresh cucumber slices, and tomato wedges over the lettuce.
Serve: Drizzle the warm peanut sauce generously over the salad.
Top with fresh bean sprouts, quartered eggs, and a sprinkle of chopped peanuts.
Serve immediately while the sauce is warm.