Combine potatoes, lemon juice, salt, butter in a dutch oven or large pot. Add just enough cold water to cover, then bring to a boil over medium heat and cook until potatoes are tender about 20-25 minutes. Continue to cook until pan is almost dry, then add in the butter. Gently fry potatoes until crispy and browned.
Place on a platter.
While the potatoes are cooking, make the pesto. Add the chives, parsley, almonds and garlic in a food processor and chop until fine. With the machine running, gradually add lemon juice and remaining oil through feed until incorporated. Season to taste with salt and pepper.