You're going to do the same thing, which is pounding and grinding the ingredients together in a pestle mortar, into a paste. Here is how I like to do the sequence of the ingredients.
The garlic cloves and salt.
The anchovies.
The parsley.
The basil. I like to add the basil in batches to make it easier.
The walnuts.
Parmesan. This also, I like to add in batches to make it easier.
The extra virgin olive oil. I add this bit by bit, it's easier to mix.
You can, of course, put everything in a food processor and blend away.
Notes
Don't worry about the anchovies fillets being used in this recipe. They don't add any fishy taste at all. Instead they add this creamy saltiness aspect to this delicious pesto.