Spread the tofu slices in a single layer over a paper towel–lined baking sheet and let them drain for 20 minutes. Press the slices dry with more paper towels, season with salt and pepper, and dredge in cornstarch until evenly coated.

Combine the carrots, cucumber, lime juice, and fish sauce in a bowl and let the mixture sit for 15 minutes to pickle. In a separate bowl, whisk the mayonnaise, Sriracha, and lime zest together until smooth.

Heat the oil in a 12-inch nonstick skillet over medium-high heat until the oil shimmers and just begins to smoke. Add the tofu and cook until both sides are crisp and deeply browned, about 4 minutes per side.

Spread the mayonnaise mixture evenly over the cut sides of each roll. Layer the tofu, pickled vegetables (discarding the liquid), and cilantro between the rolls. Press gently on the sandwiches to set the layers and serve immediately.