Place hamburger, garlic and ginger in a medium pan on medium heat.
Break up burger and stir occasionally as hamburger browns (if hamburger has high fat content, drain excess fat before proceeding).
Mix soy sauce, cornstarch, brown sugar, and beef broth in a small mixing bowl. Add 1-4 teaspoons cayenne pepper, to your taste.
Add sauce mixture to pan; heat on medium heat until sauce thickens, stirring continually.
Stir in scallions, reduce heat to low and simmer ~15 minutes (reserve some of the green onion slices for garnish, if you wish).