Season turkey breasts with salt, pepper, and oregano.
In a large oven-safe skillet on high heat pan sear turkey breasts in butter until golden brown on both sides (10 minutes total).
Place the skillet in the oven and cook at 375 degrees for 20 minutes or until the turkey reaches and internal temperature of 170 degrees. Remove the turkey breast from the skillet and place on a cutting board to rest for 10 minutes.
Return the skillet to high heat and add in the sliced onions. Once the onions begins to turn golden brown, reduce to medium heat and saute for 5 minutes, or until the onions are soft.