Preheat oven to 400. Add walnuts to a sheet pan and bake for about 7 min or until toasted. Remove. Use 1/4 cup for crust and roughly chop. Set the other 1/4 cup aside for the pesto.
Lay out puff pastry on parchment paper and lightly score the sides with a fork. Brush egg wash over crust and then top with chopped toasted walnuts
Make your leek pesto by first cooking your leeks. Wash leeks thoroughly and then chop into coin shapes. Discard green ends. Add EVOO to a pan and add leeks. Season with salt and pepper and cook until slightly browned. In a food processor, combine cooked leeks, the remaining walnuts, olive oil, lemon juice, basil, parmesan, salt and pepper. Blend until combined. Taste and adjust accordingly to taste.
Spread over puff pastry. Top with gruyere. Crack and egg over the top. Use the cheese to create little walls so your egg stays in the middle of the pastry.
Transfer to a parchment lined baking sheet and bake for about 10 min or until egg is cooked on top. Remove and top with hot honey chili crisp. Eat right away. Enjoy!