Soak the raw cashews in hot water for 20 minutes, drain then transfer to a powerful blender (I love my Vitamix for this) with the rest of the ingredients. Puree until fluffy and smooth on the smoothie setting. Refrigerate until needed.
Prepare the Salad:
Peel the carrots and rinse them well together with the potatoes. Use a sharp knife and cut them into small dice. Transfer to a medium soup pot and cover with water. Add the bay leaves and a pinch of sea salt then bring to a simmer. Boil until tender but not mushy. Drain in a colander, discard bay leaf and allow the veggies to dry off in their own steam for a few minutes.
If using frozen peas just run them under some hot water to defrost fora minute or so or add them to the pot with the potatoes and carrots in the last minute of cooking. If using fresh green peas you can chose to steam them separately or cook them with the potatoes and carrots for a few minutes.
Transfer the cooked potatoes, carrots and peas to a large mixing bowl together with the chopped cornichons (or roasted peppers). Drizzle with the aioli mayo and combine until all the veggies are coated well. Add in the fresh dill and adjust seasonings with sea salt and black pepper.
Serve with a sprinkling of fresh chives on top.
if you like to thin out the aioli you can do so by adding some of the pickling juice from the cornichons or roasted peppers.