Trim tenderloin of all fat and silver skin and cut each end off about 3-4†to make it the same diameter from end to end. Reserve ends for future use. Tie the tenderloin crosswise at 2-inch intervals using cotton twine. Sprinkle roast evenly with 2 teaspoons of salt, cover loosely with plastic wrap, and let stand at room temperature 1 hour. In a small bowl, mix the pepper, garlic, and remaining salt with 4 tablespoons salted butter. Pat the meat dry with paper towels and rub the tenderloin with the butter mixture. Put the tenderloin on a wire rack set in a rimmed baking sheet in the preheated 300 degree F oven. After about 20 minutes, flip tenderloin. Roast until instant-read thermometer inserted into center of roast registers 135-140 degrees F, about 55 to 60 minutes. The tenderloin will continue to cook after removing it from the oven, so take it out about 10 degrees rarer than you want to serve it. Transfer roast to cutting board and spread 2 tablespoons shallot-parsley butter evenly over top of roast; let rest about 10 minutes. Remove twine and cut meat crosswise into ½-inch-thick slices.