Slice the heads of romaine in half lengthwise, remove the root end, and separate the leaves. Wash and dry them carefully.

Cut the shrimp in half lengthwise and season with salt and pepper. In a small skillet, sauté the shrimp in the olive oil over medium-low heat. As soon as they turn opaque, remove them from the pan and set aside to add to the finished salad.

Peel the mango with a vegetable peeler and cut the broad sides into 1/8-inch-thick slices. (The narrow sides tend to be fibrous and difficult to slice.) Cut these slices into ¼-inch-wide strips and set aside.

Cut the avocado in half lengthwise and remove the pit. Cut into ¼- inch-thick slices, leaving the skin intact. Sprinkle lightly with lime juice.

Put the shallot in a large bowl with the vinegar, remaining lime juice, ginger, and jalapeño. Season with salt and macerate for 15 minutes. Whisk in the extra-virgin olive oil and lime zest. Add the shrimp and mango strips and scoop the avocado slices out of their skin into the bowl. Toss gently and serve sprinkled with chopped cilantro.