Bring a large pot of water to a boil and cook the noodles according to package directions. Drain and set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced beef and cook until browned on both sides, about 3 to 4 minutes. Remove the beef to a plate.
Add the remaining tablespoon of vegetable oil to the skillet. Stir in the garlic and ginger and cook for 30 seconds until fragrant.
Add the broccoli florets and cook for 3 minutes, stirring often, until they turn bright green.
Return the beef to the skillet. Pour in the soy sauce, hoisin sauce, and honey. Stir to coat everything.
Add the cornstarch mixture and stir until the sauce thickens, about 1 minute.
Remove the skillet from heat and stir in the sesame oil. Serve the stir-fry over the cooked noodles.