Place almonds in a processor and process for 1 minute, until finely chopped. Add garlic and process for 10 more seconds.
Add basil, parmesan, lemon zest and juice, salt and pepper. Process, for 10 more seconds then with the processor running, drizzle in the olive oil in a slow steady stream.
Once all the olive oil is added, stop and scrape down the sides of the bowl. Process again until the ingredients are almost smooth. Add up to ¼ cup more olive oil depending on how thick or thin you want the pesto.