Mix the soy sauce, oyster sauce, honey, cornstarch, water, and sesame oil in a small bowl. Stir it until the cornstarch dissolves completely — this is your sauce, and it's gonna be so good. Set it aside and forget about it for now.
Heat 1 tablespoon of oil in a large skillet or wok over high heat until it's really hot (about 2 minutes). You'll see it shimmer and kinda move around the pan. Don't skip this step because cold oil won't sear the beef properly.
Add the beef strips in a single layer and let them sit for 2-3 minutes without touching them. This creates that gorgeous golden crust you're after. Then flip and cook another 2-3 minutes until cooked through but still tender.
Remove the beef to a plate and add the remaining 1 tablespoon oil to the same skillet. Toss in the broccoli and carrots, stirring constantly for about 4 minutes until they're tender-crisp (mine always stick just a little to the pan and that's totally fine).
Add the minced garlic and ginger, stirring constantly for about 30 seconds until fragrant. You'll smell how amazing it is — that's the signal you're doing it right. Don't let it burn though, so keep moving it around.
Pour the sauce into the skillet and bring it to a simmer. It'll thicken up in about 1-2 minutes and coat everything beautifully. The beef and broccoli recipe comes together right here.
Return the beef to the skillet and toss everything together for about 1 minute. Taste it and adjust the soy sauce if you want it saltier, or add a touch of honey if you prefer it sweeter. Serve it immediately over rice or noodles.