Slice away and finely chop the chard stems. Coarsely chop the leaves. Heat 2 tablespoons oil in a small skillet. Add the stems and 2 tablespoons shallots. Sauté on medium until soft but not browned.
Transfer to a food processor. Add the leaves and a few tablespoons water to the skillet and cook on medium-high a few minutes, until they wilt.
When the chard leaves are cool enough to handle, squeeze out all liquid (a potato ricer works well). Add the drained leaves to the food processor with the stems and purée. Add half the anchovies, the crème fraîche and 1 1/2 tablespoons butter. Process briefly and transfer to a small saucepan.
Heat oven to 450 degrees. Rub the beef with the remaining oil and season with salt and pepper. Over medium-high heat, warm a nonreactive oven-proof pan that will hold the beef comfortably. Brown the beef on all sides, about 5 minutes. Place the pan in the oven and roast to an internal temperature of 115 degrees for medium rare, about 15 minutes (for medium, roast 5 minutes more). Transfer the beef to a cutting board to rest.
Reheat the Swiss chard mixture and keep warm. Add the remaining shallots to the pan used for the beef and cook on medium heat until soft. Stir in the remaining anchovies and thyme. Add the vinegar, increasing the heat and cooking until it just slicks the pan. Add the wine, cook a few minutes, then swirl in the remaining butter in bits. Cook until the sauce thickens a bit. Season to taste with salt and pepper.
Spread the Swiss chard along one side of a small platter or each of two dinner plates. Cut the beef in six thick slices and arrange partly on the chard. Spoon the sauce along the other side of the beef.
