Preheat oven to 375'F. Pat potatoes with paper towels to remove excess water. Spread potatoes out in an even layer on a greased baking sheet. Put potatoes in oven and bake for about 30 minutes, or until potatoes are cooked through, lightly browned and crisp. Set potatoes aside until cool enough to handle.
Meanwhile, in a small bowl, whisk together the reserved brine from olives and oil from tuna to make a vinaigrette dressing, set aside.
Slice the hardboiled eggs into 12-15 thin slices.
Blanche the green beans (submerge into boiling water for 1-2 minutes until bright green, then plunge into ice water to stop the cooking, pat dry, set aside).
Pull apart the potatoes and pile into 12-15 small "haystacks".
Drizzle each haystack with a little bit of the vinaigrette, pile about a teaspoon of tuna on top, top the tuna with about a teaspoon of olive, top the olive with a slice of egg, top the egg with 2 green beans, then drizzle with a little bit more of the vinaigrette. Continue this process until you have 12-15 little nicoise salad haystacks. Remove to serving plates with a flexible spatula. Serve as appetizers.
Note: these are meant to be 1-2 bites. although a little messy, we just picked them up and ate them in one bite, it's all the flavors together that makes them so yummy.