Heat the broiler to low and arrange the rack in the top of the oven.
To butterfly the pork, place the tenderloin on a cutting board with one end pointing toward you. Slice lengthwise down the center of the tenderloin, almost but not quite cutting through it, leaving about 1/8- to 1/4-inch thickness of meat intact.
Open the tenderloin up like a book and push on it to flatten.
Starting on the right side, with the blade of the knife perpendicular to the cutting board, make a 1-inch-deep incision down the length of the seam, being careful not to cut through the meat.
Push to flatten. Rotate the tenderloin and repeat on the uncut side along the seam.
Place the tenderloin on a baking sheet.
Combine the mustard and olive oil and rub it on top of the pork, then season well with salt and freshly ground black pepper. Place the tenderloin under the broiler and cook until the top is light golden brown, about 8 minutes.
Remove from the broiler and place on a cutting board. Cover the pork loosely with foil and let it rest for 5 minutes. Slice against the grain and place on a platter. Serve with salsa verde.
Beverage pairing: This dish has great balance on its own, so a balanced wine is also called for. Pork can often go with red or white wine; the salsa verde may push in the direction of the latter. However, a light, lean, and earthy red might be a little more interesting. Use the mustard as a jumping off point and go with a simple red from the region of Dijon, Burgundy. Try the 2005 Bourgogne Passetoutgrain from Domaine Jean Tardy, a bright, juicy blend of 50 percent Pinot Noir and 50 percent Gamay from one of the top producers in the region.
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