Prepare a grill for medium-high heat. Put the tofu between 2 plates, and weight the top plate down with about 4 pounds (3 large cans or a large, heavy skillet) for about 20 minutes to remove excess moisture.
Meanwhile, whisk together 1/2 cup of the vinegar, 1/2 cup water, the sugar and 1/2 teaspoon salt in a medium bowl until the sugar and salt dissolve. Add the carrots and cucumbers, toss to coat and chill until ready to serve.
Whisk together the mayonnaise and Sriracha in a small bowl; set aside.
Pat the tofu dry, and cut it into 8 1/2-inch-thick slices. Grate the garlic into a large bowl, and stir in the hoisin, the remaining 3 tablespoons vinegar and the oil. Add the mushroom caps, and stir to coat. Lightly oil the grill grates.
Shaking off any excess marinade, put the mushroom caps on the grill. Grill them for about 1 minute, rotating them once to char more of the cap, then flip and cook until almost tender, 30 seconds to 1 minute more. Transfer the mushrooms to a platter, and sprinkle lightly with salt and pepper.
Toss the tofu in the marinade, then grill, marinade-side down, for 2 minutes. Flip, and grill the second side for 2 more minutes. Transfer the tofu to the platter.
Open the rolls, and grill, cut-side down, until just toasty, about 2 minutes.
Smear each half of a roll with 1 heaping tablespoon of the mayonnaise mixture. Put 2 pieces of tofu on each roll, then shingle the mushrooms, overlapping slightly, on top. Top with some of the carrot-cucumber salad, drained, and a shower of cilantro leaves. Close the rolls, pressing gently. Halve them on the diagonal, and serve.
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