Heat the broiler to medium and arrange a 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, almost but not quite cutting through the tenderloin, leaving about 1/4- to 1/2-inch thickness of meat intact.
Open the tenderloin up like a book and push on it to flatten.
Starting on the left side, with the blade of the knife parallel to the cutting board and the blade facing left, slice down the length of the seam, maintaining the 1/4- to 1/2-inch thickness.
Pull the meat open and press down to flatten. Continue cutting and flattening until the entire left half is 1/4- to 1/2-inch thickness. Rotate the tenderloin and repeat on the other half.
Lightly coat a baking sheet with olive oil and place the tenderloin cut-side down on the baking sheet.
Combine the mustard and measured olive oil in a small bowl and rub it on top of the pork, then season the meat well with salt and pepper. Place the tenderloin under the broiler and cook until the top is light golden brown, about 12 to 15 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.