Season both sides of the filet mignon with salt and pepper. Allow to sit at room temperature for 30 minutes to 1 hour.
Preheat the grill or grill pan to medium high heat.
Place steaks on the grill and cook for 3-4 minutes on each side for medium rare. Place steaks on a plate and cover with foil.
In a small saucepan, add the olive oil over medium high heat. Once shimmering, add in the shallots and cook, stirring frequently for 2-3 minutes or until softened.
Add in the Worcestershire sauce and beef broth and bring to a simmer. Meanwhile, whisk together the water and cornstarch into a slurry.
Once mixture is simmering, add in the slurry mixture, whisking constantly until slightly thickened. Remove from the heat and stir in chocolate, stirring until fully melted.
Plate steaks and serve chocolate sauce on top.