If using Chinese broccoli, trim 1/2 inch from bottoms of stalks; discard. (Stalks more than 1/2 inch in diameter should be halved lengthwise.) Slice stalks into 2 1/2 x 1/4-inch sticks. (With regular broccoli, just use the florets.)
Combine 6 cups water and 1/2 teaspoon salt in a large pot over high heat; bring to a boil. Add the broccoli stalks (or florets); blanch 2 minutes. Remove and drain in a colander. Add the leaves to the pot; blanch 1 minute. Drain broccoli in a colander.
Heat the canola oil in a large nonstick skillet over medium-high heat. Add the ginger; stir-fry 15 seconds. Add broccoli, remaining 1/2 teaspoon salt, oyster sauce, and sugar; stir-fry 1 1/2 minutes, or until broccoli is crisp-tender. Remove from heat; drizzle with sesame oil.