Blanch the basil - Plunge the basil stems into boiling water for no more than ten seconds. Pull the leaves off the stems, and measure out 4 packed cups of blanched basil leaves.
Blend the pesto - Drop the garlic cloves into the food processor while it's running and continue running until the garlic has stopped moving and bouncing off the sides of the bowl. Add the lemon juice, salt, and basil, and pulse to combine.
Finish the pesto - With the food processor running, pour in the olive oil in a steady stream. Add the cheese, and pulse to combine.
Notes
When I blanch the basil, I plunge the whole stem into the water. I don't pick off the individual leaves and measure out four cups until after the blanching process. This approach isn't precise, so it's better to pick too much than not enough. You will find a way to use it.