Place the potatoes and eggs in a medium pot; cover with water. Bring to a rolling boil, then turn off the heat, cover tightly and let stand for 10 minutes. Remove the eggs (leave the potatoes in the water) and peel them under cold water. Cut into small cubes. Remove the potatoes and dice.
Meanwhile, bring a large pot of water to a boil, salt it, add the green beans and parboil for 4 to 5 minutes. Strain out the beans, reserving the pot of water. Shock the beans in cold water, then cut into thirds.
Return the reserved pot of water to a boil, add the pasta and cook until al dente. Drain, reserving 1/2 cup of the pasta cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 4 turns of the pan, over medium heat. Stir in the anchovy paste (or fillets), if using. Add the tomatoes, wine, olives, chile pepper, shallot, garlic and herbes de provence; cover the pan and increase the heat to medium-high. Cook, uncovering the pan when the tomatoes start to crack, for about 10 minutes. Lightly crush them with a wooden spoon. Add the tuna, parsley and tarragon (or basil). Stir in the reserved pasta cooking water.
Add the pasta to the sauce and toss well. Add the green beans, potatoes and eggs.