How to create depth and drama with a single off-camera flash?

[LarryEM]

I'm a hobbyist photographer trying to improve my portrait work, and while I understand the basics of three-point lighting, I'm struggling to create more dynamic and moody looks, especially with a single off-camera flash. My home studio is just a spare room with white walls, and my portraits often end up looking flat or overly harsh. For photographers who specialize in portraits, what are your go-to portrait lighting techniques for creating depth and drama with minimal gear? How do you modify a single light source effectively, and what are the most common mistakes beginners make when trying to emulate high-contrast or Rembrandt-style lighting that I should avoid?