Boil the cubed potatoes with sea salt until done but not falling apart. Drain well and set aside to cool off.
Cook the peas in a small pan with some water until slightly tender. Drain and set aside.
Chop 3 of the hard-boiled eggs in small cubes. Slice the remaining egg and set aside (used for garnishing)
Cut in small pieces the Giardiniera and add them to a large bowl. Add the peas, tuna, rinsed caper, mustard, chopped eggs, chopped cornichons, salt and pepper, half of the mayonnaise. Mix well.
Add the cooled diced potatoes to the bowl and mix well. Add more mayonnaise as you go along until you have a soft consistency salad. Taste to adjust the flavor
Let the insalata rest in the refrigerator for at least 1 hour, decorate with the sliced egg and serve.