Scrub the potatoes to clean off any lose dirt and sand.
Pour water into a large pot, cover and bring to a boil on high heat. Place potatoes in the pot and boil them with skins on until they are cooked, but not too soft. Test the doneness by pricking with a fork to make sure they are cooked, but still firm. Don’t overcook the potatoes or you’ll end up with mashed potatoes when mixing your salad.
Drain the water from the pot and add cold water to the pot, covering the potatoes. Change water every few minutes until the potatoes are cool enough to handle with your bare hands. Refrigerate for a few minutes to cool further.
Remove from refrigerator and peel potatoes. Cut into small (approximately 1/2″) cubes. Return to refrigerator while you prepare the other ingredients.
Put approximately 1 1/2 cups of mayonnaise into a bowl. Slice 1 of the roasted pepper into strips about 1/3 inch wide, then cut into smaller pieces and add to bowl.
Drain tuna thoroughly, then flake with a fork and add to bowl.
Drain carrots and peas and add to bowl.
Peel 1 egg, chop and add to bowl.
Mix all ingredients together.
Add the mayonnaise mixture to the potatoes and mix thoroughly. If necessary, add more mayonnaise. Smooth top of potato salad, preparing for decoration.
Traditionally, a thin layer of mayonnaise is spread over the top of the salad using the back side of a large spoon. Slice remaining red pepper into thin strips and arrange on top of salad. Drain the white asparagus and olives. Carefully slice hard-boiled eggs Use to decorate the salad.