Preheat oven to 425°F (218°C).
Pat the beef dry with paper towels and season all sides generously with salt and pepper.
In a large oven-proof skillet, heat olive oil over medium-high heat until shimmering.
Sear the roast on all sides until a dark brown crust forms, approximately 12 minutes in total.
Transfer the skillet to the oven and roast until the internal temperature reaches 125°F (52°C) for medium-rare, approximately 20 to 25 minutes.
Remove the roast from the skillet, transfer to a cutting board, and tent loosely with foil for 15 minutes.
Place the skillet on the stovetop over medium heat, add butter and shallots, and sauté until translucent.
Deglaze the pan with white wine, scraping the bottom to release the fond, and reduce liquid by half.
Whisk in the heavy cream, Dijon mustard, and whole grain mustard; simmer until the sauce thickens enough to coat the back of a spoon.
Stir in the fresh tarragon and chives, then season with salt and pepper to taste.
Slice the rested beef into 1-inch thick medallions and serve immediately with the warm mustard sauce.