Heat a non-stick pan on the stove on medium heat
Add the walnuts to the pan and gently toast the walnuts for approximately 5 minutes moving them around so they don't burn, take care not to burn as they will turn bitter.
Remove from the heat once they have toasted and leave to cool before roughly chopping the walnuts
Place basil leaves, garlic, cooled toasted walnuts and salt into a food processor and pulse a few times scrape down the sides.
Slowly stream in the olive oil so that the oil doesn't seperate. Occasionally scrape down the sides so it all mixes together.
Add the pepper and grated parmesan cheese and pulse to mix.
Taste and add more salt and pepper to taste if needed
To store pesto in the fridge: Pesto darkens if exposed to air so place in a jar and either cover with cling film making sure it is touching the pesto or top up with more olive oil. This will keep in the fridge for 2-3 weeks
To Store in the freezer - you can easily store pesto ion the freezer but if you are freezing then do NOT add the parmesan cheese as it does not freeze well. You can add the parmesan after defrosting, simply stir through the parmesan once pesto has fully defrosted and check the seasoning, adding extra salt and or pepper to taste.