I put basil, cheese, nuts and garlic into the food processor. Pulse. Then turn on low and pour the olive oil in. I stir n salt and pepper by hand.

I don't add cheese (my cousins in Italy never do, that's where I learned to make it)

My food processor recipe calls for:
grind pignioli, then remove and put aside
salt and garlic first (pulse)
add basil and 1/2 olive oil (grind)
add rest of olive oil while grinding
then add the nuts. (pulse a few times to mix)

I like the idea of the basil and oil being added at the same time, so that the basil gets a coating, kind of the way you coat salad greens with oil before adding the vinegar or salt.