Heat olive oil in a sauce pan over medium-high heat. Add onion, carrot and celery. Sauté for 5-6 minutes until brown. Add garlic and peppercorn and sauté for 2-3 minutes. Deglaze pan with brandy and allow to reduce almost completely.
Place stock and basil into pan, allow to reduce by half. Strain mixture, then return to sauce pan over medium heat and finish with butter, whisking to combine. Set aside.
Cut a pocket in the top of the filet and fill with boursin cheese. Season each side of the filet with salt and pepper.
In a skillet, heat olive oil over high heat. Place filet stuffing side down in order to caramelize the cheese (this will prevent cheese from running out). Turn the filet over, making sure both sides are browned.
Place the filet cheese side up on a roasting pan or in a skillet into a pre-heated 325° oven until it reaches your desired temperature, then remove and serve with 2 ounces of poivre vert sauce.
