Heat a medium (10 to 11-inch) dry cast-iron skillet over high heat for 3 minutes. Brush the tuna all over with olive oil and sprinkle it generously with salt and black pepper. Sear the tuna in the skillet for exactly one minute on each side. (The inside will be raw.) Transfer to a cutting board, cut into 1/2 to 3/4-inch dice, and set aside.
In a large bowl, combine 1/4 cup olive oil, the lime zest, lime juice, soy sauce, Tabasco, 1 1/2 teaspoons salt, and 1 teaspoon black pepper. Add the tuna, scallions, and jalapeño. Cut the avocado in half, remove the pit, peel, and cut 1/2 to 3/4-inch dice. Carefully stir the avocado into the tuna mixture and set aside for 20 minutes.
Meanwhile, combine the shallot and vinegar in a small bowl and set aside.
Place the butter in a large (12-inch) sauté pan over medium-high heat and heat until the butter sizzles. Without opening the buns, toast them on each side for one minute, until nicely browned. Line the buns up on a platter, cut sides up, and spoon the tuna mixture into the buns. Drizzle with the Chipotle Mayonnaise and sprinkle on the pickled shallots. Serve while the buns are warm.
Place the mayonnaise, chipotle pepper, adobo sauce, lime juice, and 1 1/4 teaspoons salt in the bowl of a food processor fitted with the steel blade. Process until smooth. Refrigerate for up to a week.