Slice beef thinly against the grain. Marinate in 2 tablespoons soy sauce, half the garlic, and half the ginger for 15-30 minutes if time allows.
Whisk together sauce with remaining soy sauce, hoisin sauce, sesame oil, honey, and remaining garlic and ginger. Set aside.
Heat wok or skillet over high heat until almost smoking. Add 1 tablespoon vegetable oil.
Sear beef in single layer for 2 minutes without stirring, then flip and cook 1 more minute. Remove to plate.
Add remaining oil to pan. Stir fry carrots, bell pepper, and broccoli for 3-4 minutes.
Add snap peas and cook 2 more minutes until vegetables are tender-crisp.
Return beef to pan with prepared sauce. Stir everything together and cook 1-2 minutes until sauce thickens slightly.
Garnish with green onions and sesame seeds. Serve over steamed rice.