Add basil, walnuts, garlic cloves and salt to a food processor or blender. Pulse to combine.
When things are chopped well, start slowly adding your olive oil while the processor/blender is running on low. This starts to form an emulsion and gives you the consistency you would want.
When the pesto is smooth and has a thickened consistency, remove from processor/blender to a bowl add parmesan cheese, and stir.
Taste the fully combined pesto and add any additional salt and pepper that you think it might need. Store in the fridge for a few days.