Fill a bowl halfway with ice and enough water to cover ice. Add ½ teaspoon salt for each quart of water. Set aside.
In a saucepan over medium heat, bring 3 cups of salted water to a boil. Add carrots and cook for about 1 minute or until half done. With a slotted spoon, remove from pan and plunge into bowl of ice bath.
Add broccoli and cauliflower to the boiling water and cook for about 2 to 3 minutes or until half-done. With a slotted spoon, remove from pan and plunge into the ice bath.
Add cabbage to the boiling water and cook for about 30 seconds or until half-done. With a slotted spoon, remove from pan and plunge into the ice bath.
Add peppers to the boiling water and cook for about 30 seconds or until half-done. With a slotted spoon, remove from pan and plunge into the ice bath.
Reserve 2 cups of the poaching liquid (the one used to blanch vegetables).
Drain vegetables from the ice bath when they are cold.
In a wok or wide skillet over medium heat, heat about 2 tablespoons of the oil.
Add chicken liver in a single layer and fry until lightly browned on all sides but not fully cooked. Remove from pan and keep warm.
Discard excess oil and wipe down the pan. Add the remaining 1 tablespoon of oil and heat.
Add onions and garlic and cook until softened.
Add chicken and cook, stirring regularly, until color changes.
In a bowl, combine the reserved poaching liquid and oyster sauce. Add to the pan and bring to a boil. Continue to cook, skimming scum that may float on top, for about 4 to 5 minutes or until chicken is cooked through.
Add the liver and cook for 1 to 2 minutes.
Add parboiled vegetables, baby corn, and quail eggs, stirring gently to combine, and cook for about 3 to 5 minutes.
In a bowl, combine ¼ cup of cold water and corn starch and stir until corn starch is dissolved. Add mixture to the pan, stirring gently. Cook for about 1 to 2 minutes or until sauce is thickened.
Season with salt and pepper to taste. Serve hot.