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Step 1
Separate the broccoli florets from the stems. Pare the stems with a paring knife or vegetable peeler and cut them into 1/4-inch slices on the diagonal. Separate the floret clusters into smaller florets (1 inch wide) and halve them lengthwise if large. The pieces need to be small to cook quickly, but not so small that they risk getting overcooked. (see Cutting broccoli so it cooks evenly)
Step 2
In a small bowl, stir together the stock and cornstarch until the cornstarch dissolves. Add the oyster sauce and toasted sesame oil and stir to blend.
Step 3
Heat a large wok (or high-sided skillet) over high heat. When the skillet is hot, add the peanut oil and swirl to coat. When the oil is hot, add the garlic, ginger, and chile (if using) and stir-fry for 15 seconds to release the garlic’s fragrance. Be careful not to let the garlic burn. Add the broccoli stems and florets and stir-fry until crisp-tender, about 3 min., adding water, 1 to 2 Tbs. at a time, if needed. Add the oyster sauce mixture and stir-fry for about 30 seconds to allow the cornstarch to thicken the sauce lightly. Immediately transfer to a warm platter and serve.