Spread tofu on a paper towel lined baking sheet and let drain for about 20 minutes. Gently press dry with a few more paper towels and season with salt and pepper.
Combine the carrots, cucumber, lime juice, and fish sauce in a large bowl; let sit for 15 minutes. Whisk together the mayonnaise, Sriracha, and lime zest in a second bowl.
Spread cornstarch in a shallow dish then dredge the seasoned tofu then transfer to a plate.
Heat the olive oil in a large skillet over medium-high heat until just smoking. Add in the tofu and cook until crisp and browned, about 4 minutes per side; transfer to a paper towel lined plate.
Spread the "mayo" mixture evenly over cut sides of each roll. Layer tofu, pickled vegetables, and cilantro evenly in rolls. Press gently on sandwiches to set; then serve. Enjoy!