Pat steak with a paper towel to remove excess moisture.
Season both sides of steak with salt and pepper. Let sit for 5 minutes.
Heat oil in cast iron skillet over medium-high heat.
Add steak, two springs of thyme and 2 tablespoons butter and cook until well browned (about 3-5 minutes depending on the thickness.). Tilt the pan and spoon juices over steak occasionally.
Flip steak and repeat with the opposite side.
Using tongs, sear the sides of the steak.
Transfer to plate and tent loosely with foil.
Add 1 tablespoon of butter to the empty skillet and melt over medium-high heat.
Add shallot and cook until fragrant and soft, approximately 3 minutes
Add wine and brown sugar, simmer until reduced, approximately 3 minutes.
Add broth and simmer until the mixture is reduced by 1/2, approximately 5 minutes.
Remove from heat.
Add in butter and minced thyme, mix well and set aside.
Slice steak into 1/4 inch slices. Place on serving dish and cover with red wine sauce.