Preheat the oven to 80°C (176°F). Place a casserole dish on the oven floor to catch drippings from the beef.
Peel and finely chop the shallots and garlic. Season the beef fillet with salt and pepper. Heat a large pan over medium-high heat with a thin film of olive oil and sear the beef fillet for about 5 minutes, turning occasionally, until browned on all sides.
Transfer the seared beef to a wire rack positioned in the oven above the casserole dish. Cook for 1 hour 45 minutes.
Return the same pan to medium heat. Add the chopped garlic and shallots and fry for about 2 minutes until soft and fragrant.
Add the tomato paste and stir constantly for 1 minute. Pour in the red wine, scraping up any browned bits from the bottom of the pan. Increase heat to medium-high and reduce the wine by about half, approximately 5 to 7 minutes.
Add the veal stock and simmer over medium heat, stirring occasionally, for 5 to 10 minutes until about 200 ml of liquid remains. Strain the sauce through a sieve into a small saucepan. Stir in the rinsed pickled red peppercorns and balsamic vinegar.
Just before serving, bring the sauce to a gentle boil over medium heat. Reduce heat to low and whisk in the cold butter piece by piece until fully combined and silky. Season with salt and pepper to taste.
Slice the beef fillet and arrange on preheated plates. Pour the sauce over the meat. The beef will be very rare and deep red in color due to the low oven temperature—this is normal.
Serve with a salad of your choice or with beans as a side dish.