Mix the minced sun-dried tomatoes with 2 Tbs. of the butter and the vinegar. Season with a pinch or two of salt, wrap in plastic, and mold into a 2-inch-long cylinder. Put in the freezer to firm.
Season the beef well on both sides with salt and pepper. In a large skillet over medium-high heat, heat the olive oil until quite hot. Sear the beef medallions until well browned on both sides and cooked to rare, about 2 minutes per side (or longer if you like your steak cooked more). Transfer to a plate and tent with foil to keep warm. Add the remaining 2 Tbs. of butter to the pan. When it’s foaming, add the shallots, cook for 30 seconds, and add the mushrooms and a good pinch of salt. Sauté until the mushrooms are well browned, 2 to 3 minutes. Add the arugula to the pan and toss with the mushrooms, cooking just until the leaves have wilted. Arrange the sauteed vegetables on dinner plates, top with the beef, and serve with a slice or two of the chilled butter on the beef.
nutrition information (per serving):
Photo: Scott Phillips