Preheat oven to 350oF (180°C).
Place potatoes into a pot of cold, salted water and bring to a boil. Reduce heat and cook potatoes until fork tender. Remove from heat, drain and set aside.
To make pesto: Add 3 tbsp of olive oil, basil, salt, pepper, lemon juice, lemon zest and garlic to a blender, and pulse until all ingredients are incorporated. Add half of the walnuts and pulse until mixture is coarse.
Place potatoes in a bowl and toss with remaining olive oil. Transfer to a glass cooking dish and roast in the oven for 30 minutes, or until skins are crispy.
Remove from the oven. Place potatoes in a large bowl and mix with pesto and remaining walnuts. Enjoy!