For the tuna conserva: Put the olive oil, salt, peppercorns, bay leaves, garlic, fennel and onions in a 6- to 8-quart saucepot. Bring to a low simmer over medium heat and cook until the onions and fennel are tender. Carefully place the tuna in the pot and cook for 5 minutes. Remove from the heat, cover halfway with a lid and let sit until cool to the touch, about 2 hours.
Remove the tuna and pull it apart into medium-size chunks. Reserve 8 ounces for the salad, and divide the rest among small mason jars (or other airtight containers). Pour the contents of the saucepot over the tuna, dividing it evenly among the jars.
For the anchovy vinaigrette: Combine the anchovies and their oil, parsley, lemon juice and onions in a blender and puree until fully mixed. Set the blender to low speed and slowly drizzle in the olive oil until emulsified. Season with salt and pepper.
For the nicoise salad: Preheat the oven to 350 degrees F.
In a bowl, toss the potatoes and tomatoes in some olive oil, season with salt and pepper and place on a baking sheet. Roast the tomatoes about 30 minutes and the potatoes until tender. Let cool.
Combine the reserved tuna conserva, potatoes, tomatoes, haricot vert, olives, chives and Bibb lettuce leaves in a mixing bowl and dress with 1 cup of the anchovy vinaigrette. Season with salt and pepper.
Divide the salad evenly between two plates, arranging the mixture to best present each ingredient. Place 2 egg halves on each plate and serve.