Bring a pot of water to boil and add the broccoli florets. Boil for 2 minutes, or until slightly tender and bright green. Drain then transfer the broccoli florets to a bowl of ice water to stop the cooking. Drain again and set aside.
Meanwhile, whisk together the beef stock, oyster sauce, brown sugar, mirin, and cornstarch in a large measuring cup or bowl. Set aside.
Heat the vegetable oil over medium high heat in a large wok or skillet with high sides. Add the beef and break it apart into large chunks spread evenly across the pan. Cook, undisturbed, for 2-3 minutes, or until the bottom is browned. Stir and break the beef up into smaller chunks, continuing to brown for another 2-3 minutes. Drain any excess fat off the pan.
Stir in the garlic, sauteeing until fragrant, about 30 seconds. Add the soy sauce and sesame oil, stirring until the beef is well coated.
Add the broccoli to the pan, then pour in the sauce mixture, scraping up any browned bits off the bottom of the pan.
Cook for about two minutes, continuing to stir and scrape the bottom, until the sauce is thickened. Serve warm over rice with a sprinkling of sesame seeds.
Notes
Serve with white rice or cauliflower rice. Gluten free option: Sub tamari for the low sodium soy sauce, and look for Kikkoman brand GF oyster sauce.