Step 1Combine the Shaoxing wine, soy sauce, oyster sauce, sesame oil and sugar in a medium bowl. Using a Microplane, grate the garlic directly into the mixture. Or crush into the bowl with a garlic press or mince by hand before adding. Stir until the sugar dissolves. Pour about half the mixture over the steak in a shallow dish that holds it snugly. Turn the steak to evenly coat, then marinate at room temperature while you heat the grill or cover and refrigerate for up to 1 day. If refrigerating, cover the remaining marinade and refrigerate it as well.
Step 2Heat a grill or grill pan to medium-high.
Step 3Use a sharp paring knife to cut the thick peel off the stems of the broccoli, then cut each stalk in half or quarters lengthwise. You want them all to be about the same size. Drizzle with the vegetable oil and toss to evenly coat.
Step 4Remove the steak from the marinade and pour its marinade into a cast iron or other heavy heatproof small skillet or saucepan. Add the remaining sauce to the skillet and set on the grill. Put the steak and broccoli on the grill grate in a single layer. Grill, turning once, until the broccoli is evenly charred and tender and the steak is well-seared, 10 to 12 minutes. The sauce will be simmering alongside for the same amount of time. If it starts to thicken past the consistency of syrup, pull it off the grill.
Step 5Transfer the broccoli and steak to a rimmed baking sheet and drizzle the boiled marinade all over. Let the steak rest for 5 minutes, then cut with the grain into thirds. Cut each section into thin slices across the grain and toss with the broccoli and sauce. Serve hot.