Place the potatoes in a pot and cover with cold water. Add salt and bring to a boil, then reduce the heat to a simmer and cook until the potates are fork tender, about 12 - 15 minutes. When they are done, remove them from the pot and when they are cool enough to handle, cut them in half.
Then, cook the green beans. Create an ice bath by filling a large bowl with ice water and place it next to the stove.
Refill the same pot with water and bring it to a boil. Add the breen beans and blanch for 3 minutes. Then, immediately transfer them to the ice bath. This stops the cooking and the ice water helps retain the color and al dente texture of the beans.
Make the basil vinaigrette by adding all the ingredients to a blender and blend until very smooth. Taste and adjust seasoning as necessary.
Assemble the salad. Drain the tuna. Using a fork, break it into chunks and add it to the bowl, then arrange the potatoes, green beans, cherry tomatoes, sliced red onion, hard boiled eggs and tuna in a bowl.
Drizzle the dressing over the salad, toss gently and top with freshly grated Parmigiano Reggiano and croutons and you are ready to serve.