Simple Stir-fried Udon

INGREDIENTS

• 100 g broccoli, cut into florets
• 150 g udon noodles
• 1 egg
• 2 tablespoons water
• salt
• 2 tablespoons oil, divided (olive or canola or peanut etc)
• 1 small yellow onion, chopped
• 1 stalk spring onion, chopped (reserve the green part)
• 2 garlic cloves, minced
• 3 slices ham, chopped
• 2 tablespoons hoisin sauce
• 1 tablespoon oyster sauce
• 1 tablespoon soy sauce
• 1/2 tablespoon dark soy sauce (the thick and sweet kind)
• 1/2 teaspoon white pepper
• 2 tablespoons mirin or 2 tablespoons rice wine
• crushed chili pepper flakes, to taste
• 1/2 teaspoon sesame oil
• 1 lime, juice of