Bring medium size saucepan of water to a boil. Add basil and blanch 20 seconds. Drain. Transfer leaves to processor and blend well. While machine is still running, add 1 cup oil through fed tube and blend until smooth. Season to taste with salt and pepper. Prepare a wood or charcoal fire and let it burn down to embers. For the lobsters, insert the tip of a large chefs knife just behind the head of the lobster. Cut the underside from the head to the tail. Make sure you do not cut all the way through the back shell. Spread the halves apart. With your fingers, or using a paring knife remove and discard the vein like intestinal tract that runs along the length of the lobster. Remove the small sac from behind the eyes. Do not remove the tomalley the greenishgray pancreas and liver or the dark green coral (present if the lobster is female). First, twist off the claws, then the tail. Remove the soft inside shell from the tail. Brush the lobsters with 1/2 cup olive oil and season with salt and pepper. Grill cut side up for 20 minutes. Brush some basil over the lobster. Serve passing the remaining basil oil separately. Posted to MM-Recipes Digest V4 #148 by "Vince & Juley Roberts" on May 28, 1997