Place beef in a large mixing bowl and pat dry with paper towels. Season with salt and pepper and set aside.
In a large skillet over medium-high heat, drizzle 1 teaspoon oil and cook green beans 1 minute. Add 2 tablespoons water and cover with a lid to steam, 1 minute more. Transfer green beans to a plate and discard any excess water.
Return skillet to high heat and add remaining tablespoon oil. When oil is almost smoking, add beef. Stir-fry until beef is almost cooked through, 2 to 3 minutes.
Reduce to medium heat and add garlic, ginger, soy sauce, vinegar, and monk fruit sweetener; stir quickly to coat the beef.
Add back green beans, and then top with green onions and sesame seeds. Serve immediately.