In a small pot of water, boil the eggs for 4 minutes and set aside. Bring a large pot of water to the boil and blanche the peas for 1 minute. Remove the peas from the water with a large slotted spoon and refresh with cold water. Set aside in their colander.
Boil the potatoes whole in the pot of water until cooked, about 30–40 minutes.
In a food processor, combine the basil, parsley, dill, lemon juice, Parmesan and garlic and pulse together with the olive oil until you have a rough herby pesto. Pour into a large mixing bowl.
Once the potatoes are cooked, drain them in a large colander. When they are just cool enough to handle, break them gently into bite-sized chunks with your fingers and place them in the bowl with the pesto. Season the potatoes with salt and white pepper and then very gently toss them with the pesto.
Place them on a serving platter and layer with the peas. Slice the soft boiled eggs into halves or quarters and arrange them over the salad. Give the salad a good grinding of black pepper and garnish with extra torn basil leaves and roughly chopped parsley. Give the exposed eggs a sprinkling of sea salt.