With the heel of your hand or a meat mallet, pound the meat and flatten to a thickness of about 1/2-inch. Sprinkle the inside of the meat with salt and pepper. Spread the pesto over the meat, leaving a 1-inch border on 1 long side. Roll the meat towards the border.
With your knife, mark the fillet at 1-inch intervals. Run skewers through your fillet in between your knife marks so that each portion has a skewer securing it. Using your knife marks as a guide, cut your fillet into slices. Drizzle with the oil.
Preheat the grill or a grill pan.
Grill slices over high heat for about 3 to 4 minutes per side for medium rare. Let rest for a few minutes before serving.