Cut the pressed tofu into even strips about 1/2 inch thick. Pat dry with paper towels to remove excess moisture.
In a mixing bowl, toss the tofu strips with cornstarch and a pinch of salt until well-coated.
Heat vegetable oil in a frying pan over medium heat. Add the tofu strips in a single layer and cook until golden brown and crispy, about 4-5 minutes on each side. Remove from heat and place on paper towels to drain excess oil.
In another mixing bowl, whisk together peanut butter, soy sauce, rice vinegar, honey, warm water, minced garlic, sesame oil, and chili paste until smooth. Adjust the consistency with more water as needed.
To assemble the summer rolls, fill a shallow dish with warm water. Dip one rice paper wrapper into the water for about 10-15 seconds, or until it becomes pliable. Lay it flat on a clean surface.
In the center of the rice paper, layer a small handful of shredded carrots, cucumber, bell pepper, cilantro, lettuce, and a few pieces of crispy tofu.
Fold the sides of the rice paper over the filling, then roll from the bottom up to create a tight roll. Repeat the process with the remaining wrappers and filling ingredients.
Serve the summer rolls on a plate, alongside the peanut sauce for dipping.