Place the basil leaves, spinach leaves, garlic and walnuts into the bowl of a food processor and pulse several times. Scrape down the sides of the food processor with a rubber spatula and pulse again. Slowly drizzle in the olive oil while the food processor is running until the pesto is smooth. Stir in some salt and freshly ground black pepper, to taste.
Cook on medium heat, gently moving the eggs back and forth with a spatula until they start to set, about 2-3 minutes. Cook an additional 2-3 minutes until eggs are almost set. Place the pan in oven and broil for 2-3 minutes or until the eggs are fully set and the top is golden brown.
Cut the frittata into 8 slices and garnish with pesto. Serve warm.