Toast the nuts in a small skillet over medium heat, stirring often, until just golden and fragrant, about 4-5 minutes.
Bring 4 quarts water to a boil in a big pot; lower the skewered garlic into the water, boil for 45 seconds; immediately run the garlic under cold water; remove from the skewer, peel, and mince.
Place the herbs in a quart-size zip-lock freezer bag; pound with the flat side of a meat pounder until all the leaves are bruised.
Place the nuts, garlic, herbs, oil, juice, and ½ teaspoon salt into the bowl of a fool processor.
Process until smooth, stopping as needed to scrape down the sides of the bowl.
Transfer mixture to a small bowl; stir in the cheese, and adjust seasoning with salt.
Add 1 tablespoon salt and pasta to the boiling water; cook until al dente; reserve ½ cup of the cooking water.
Drain the pasta and transfer it back to the cooking pot.
Mix in ¼ cup reserved cooking water and the pesto; use the remaining ¼ cup cooking water as needed to moisten the sauce.
Divide among 4 warmed pasta bowls; serve immediately.