Step 1

Toss the onion with 2 tablespoons of the vinegar and set in the refrigerator.

Step 2

Wash the potatoes, then put them in a small saucepan, cover with cold water, add 1 teaspoon salt, and bring to a boil. Simmer until tender when pierced with a knife, about 25 minutes, then drain.

Step 3

Bring a large pot of water to boil for the vegetables. Cut the stem ends off the beans, along with the tails if they’re tough. If the carrots are small and tender, you don’t need to peel them. Just scrub the carrots, leaving them whole or halving them lengthwise, and keep about an inch of the stems attached.

Step 4

Wash and dry the lettuces, purslane or sprouts, and herbs.

Step 5

In a mortar, mash the garlic with 1/2 teaspoon salt and 2 of the anchovies, if using. Whisk in the mustard, the remaining 2 tablespoons vinegar, and the oil, making a thick, emulsified dressing.

Step 6

When the water boils, season it well with salt, then add the beans and cook them until tender but still a little firm, 4 to 8 minutes, depending on the varieties. Scoop them out and put them on a towel to dry briefly, then toss them, while still hot, with half of the dressing. Season with salt and pepper and heap them in the center of the platter. Boil the carrots until sort of tender but still somewhat firm, 4 to 6 minutes or so, then pat dry and dress lightly, as with the beans. Set the carrots aside.

Step 7

Arrange the lettuces on the platter. Place the tuna, if using, at either end, breaking it up slightly. Halve the potatoes (or quarter them if large) and arrange them on the platter. Spoon the remaining dressing over the lettuces and potatoes and scatter the capers, if using, over all. Drain the onions and strew them on top, too. Place the remaining anchovies on top of the potatoes. Tuck the carrots and radishes into the salad, and add the purslane and herb sprigs. Season everything with pepper. Present the salad arranged. Toss before serving.