Slice the tenderloin open lengthwise, being careful not to cut through to the other side.
You want to split the meat into one large, flat piece.
Spread the mustard over both sides of the meat and rub in the pepper, pressing gently so it adheres well.
Cut the meat across into 4 even portions.
In a large skillet, heat the oil over medium heat until hot.
Put the tenderloin in the hot pan and cook, turning once, until an instant-read thermometer inserted in the thickest part reads 155°, about 10 minutes total.
Transfer the meat to a plate and tent with foil to keep it warm.
Add the broth and wine to the pan and cook over medium-high heat, scraping up any browned bits that are stuck to the bottom; continue to cook until the sauce has reduced to about 1/2 cup, 8-10 minutes.
Pour the sauce over the meat, season with salt and serve.