Before you start, rinse the basil or soak it in a few changes of water, making sure you get rid of all of the dirt.
Dry it off completely.
Next, toast the pine nuts in the toaster oven or in a dry skillet until lightly browned and color.
Set the nuts aside to cool.
Slice the garlic in half lengthwise, and remove the inner green germ.
Put the garlic in a food processor (smaller is better) along with some of the salt, and begin to grind it up to a paste.
Next, add the basil with some of the oil and continue to grind.
Toss in the pine nuts, and keep pulsing the mixture.
Add the cheese, the rest of the salt, and the rest of the oil, and finish pulsing until the mixture is still a little coarse.
Now taste it and make sure you like it!
Turn the oven broiler on high. Set the rack in the oven on the highest rung, closest to the heat source.
Rinse off the filet and dry completely. Slice the filet into four pieces horizontally. Season the fish with some salt and a squeeze of lemon juice. Drizzle with olive oil.
Broil fish on a baking tray for about 2-3 minutes, or until just cooked through.
Take out of the oven and either keep warm, or let it cool to room temperature.
Bring about a quart of water to the boil with some salt.
Cook the pasta as indicated on the package to al dente.
Drain the pasta, reserving a little bit of the cooking water, and then toss with the pesto.
Arrange slices of the fish on top of the pasta, and garnish with some fresh basil leaves.