Season flank steak on both sides with salt, pepper, and thyme.
Heat half of the oil in a skillet with a tight-fitting lid over medium-high heat; add steak and brown for 5 to 6 minutes per side; remove from pan and keep warm.
In the same skillet, heat remaining olive oil; add onion and cook until translucent.
Add 1/3 of the broth then whisk up all of the browned bits from the bottom of the pan and simmer for 2 minutes.
Place the steak right on top of the onions; cover and simmer for 20 minutes.
Remove beef and onions from the skillet and keep warm.
Raise skillet heat to medium and continue to cook the liquid remaining in the pan.
In a small bowl, combine remaining beef broth with arrowroot starch; add to the skillet, stirring constantly until thickened.
To serve, top steak portions with onions then ladle gravy on top.