Wash broccoli thoroughly under running water. Cut it into bite-sized florets. Remove the outer layer of the thick stem then cut it into thick slices.
Peel the carrot then cut it diagonally into thin slices.
Blanch
In a wok or a pot, bring about 4 cups (1 liter) of water to a full boil. Add 1 teaspoon of salt then put in the broccoli. Leave to cook for about 1 to 1½ minutes, then add the carrots and continue cooking for 1 more minute. Drain the vegetables and set aside.
Stir-fry
While waiting for the vegetables to blanch, mix oyster sauce, cornstarch, salt (⅛ teaspoon), and white pepper with water (5 tablespoons).
Heat oil in a wok or a pan over medium heat. Add garlic and sizzle it for 15 seconds or so.
Turn the heat down to low, then pour in the seasoning mixture (stir well beforehand in case any starch sinks to the bottom). Swirl with a spatula as the sauce thickens.
Put in the blanched broccoli and carrot. Toss swiftly to combine until the vegetables are evenly coated with the sauce.
Notes
Substitutes for regular oyster sauce: vegan oyster flavor sauce, mushroom vegetarian stir-fry sauce, and gluten-free oyster sauce.