Ask the butcher to spiral cut or jelly-roll cut the fillet for you to create a flat, rectangular sheet of beef.
Pound the meat with the heel of your hand to a thickness of about 1/2-inch. Season with salt and pepper. Spread the pesto evenly over the meat, leaving a 1-inch border along one of the long sides. Starting from the opposite long side, roll the meat into a log like a jelly roll.
Using kitchen string and starting 1/2-inch from one end, tie the meat in 8 places at equal intervals of approximately 1-inch. Slice between the ties to create 8 pinwheels.
Prepare a hot fire in a charcoal grill, preheat a gas grill, or preheat a stove-top cast-iron grill pan over high heat. Drizzle the meat with olive oil, then grill on both sides, turning once, until done, to your taste. Let rest for a few minutes, then remove the strings and serve.
Prepare a bowl of ice water. Bring a saucepan of water to a boil. Put the basil in a sieve and plunge it into the boiling water, pushing the leaves down into the water and stirring them so they blanch evenly. Blanch for 15 seconds, then plunge the basil into the ice water to cool quickly. Drain immediately, squeeze the basil dry, and chop it roughly.
In a blender, puree the basil with the oil, pine nuts, garlic, salt, and ascorbic acid. When well blended, add the cheese and whir briefly just to mix. Transfer to a bowl and adjust the seasoning.
Yield: about 3/4 cup, enough for 1 pound pasta.
Don't try to make this pesto in a food processor. The processor just throws it around the bowl. A blender does a much better job. Be sure to thin the pesto with some of the hot pasta water before tossing it with pasta. If your pesto typically turns army green shortly after you make it, you'll appreciate the beauty of this version. I blanch the basil briefly to set the color, and I add a pinch of powdered ascorbic acid (vitamin C), which keeps the pesto from oxidizing.
(c) NapaStyle, Inc., Sept. 2001 by M. Chiarello, D. Shalleck