Heat a large skillet or wok over medium-high heat. Add olive oil and ground beef. Cook until browned, breaking it apart with a spatula. Drain excess fat if necessary.
Add minced garlic and ginger to the skillet. Stir and cook for 1 minute until fragrant.
Stir in the broccoli florets and cook for 3-4 minutes, until bright green and slightly tender.
In a small bowl, whisk together soy sauce, hoisin sauce, sesame oil, and cornstarch slurry.
Pour the sauce into the skillet. Toss everything together and cook for another 2-3 minutes until the sauce thickens and coats the beef and broccoli.
Serve immediately over rice, noodles, or cauliflower rice. Garnish with green onions, sesame seeds, or red pepper flakes if desired.