Preheat a grill or grill pan to medium-high heat. Preheat the oven to 450 degrees F.
Brush the pork tenderloins with a little olive oil and sprinkle with salt and pepper. Grill until well-marked on all sides, about 8 minutes total.
Meanwhile, lightly dress the scallions with 1 tablespoon of the olive oil and season with salt and pepper. Grill until charred and wilted, flipping as needed. Chop the scallions really well and add to a bowl with the remaining olive oil. Fold in the sherry vinegar, chives, parsley, shallots and garlic. Set aside.
Transfer the pork to a baking sheet and brush with the mustard. Roast until the internal temperature reaches 140 degrees F for medium (to carry over to 145 degrees F), about 20 minutes. Allow the pork to rest for 10 minutes before slicing.
Serve the chimichurri on the side or on top of the sliced pork