For the roasted red peppers, preheat oven to 450 degrees. Cut peppers in half, removing seeds and stems. Cover peppers with avocado oil, and place face down on a baking sheet. Roast for about 30 minutes until a slight char begins to form on the outer skin. Remove peppers from oven, and cover in aluminum foil for 10 minutes. Peel off the outer skins.
Add walnuts to a skillet over medium-high heat, and cook for about 5 minutes until slightly browned and fragrant, stirring frequently.
Add roasted red peppers, toasted walnuts, garlic, lemon juice, basil, olive oil, salt and pepper to a food processor or high speed blender.
Mix until well combined and you've reached your desired consistency.
Transfer into a bowl, and top with kalamata olives and more fresh basil, if desired. Serve with pita chips, crackers or sliced vegetables.