Bring a large pot of water to boil, and then add spaghetti. Cook until pasta is done and then drain water and set aside.

Add avocado, parsley, garlic, walnuts and 2 tbsp cheese to a food processor. Pulse for a few moments on high speed to begin to break down the ingredients. When everything is finely chopped, gradually stream in the oil while the food processor is still running, until the sauce becomes smooth and creamy. Add in lemon juice and pulse. Taste and add salt and pepper if needed. The sauce should be thick. If you wish for a thinner sauce, add more olive oil.

Toss pasta in avocado pesto sauce. Mix in tomatoes. Garnish with parmesan cheese. Serve warm or at room temperature.