Heat the avocado oil in a skillet over medium heat. Fry the egg roll wrappers one at a time until golden and bubbly, about 15-30 seconds per side. Transfer to a paper towel-lined plate to drain. Once cooled, crumble into small crunchy pieces and set aside.
In a small bowl, make the Spicy Mayo by whisking together the vegan mayonnaise, sriracha, rice vinegar, sesame oil, soy sauce, and maple syrup until smooth. Set aside.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the garlic and cook for 2-3 minutes, stirring frequently, until fragrant.
Add the grated tofu and cook for 4-5 minutes, stirring occasionally, until lightly golden and some of the moisture has evaporated.
Stir in the cabbage and carrots. Cook for 5-7 minutes, stirring often, until softened but still slightly crisp.
Add the soy sauce, sesame oil, rice vinegar, ground ginger, maple syrup, and black pepper. Toss well to coat and cook for 1-2 minutes more. Remove from the heat and stir in the green onions.
Divide the tofu mixture among the tortillas. Top each with 1 teaspoon sesame seeds and a generous handful of the crispy egg roll pieces. Drizzle with the spicy mayo.
Fold in the sides and roll tightly into burritos.
Heat the remaining 1 tablespoon olive oil in a large skillet over medium heat. Place the burritos seam-side down and cook for 1-2 minutes, until sealed and golden brown. Turn and cook on the remaining sides until crisp and lightly browned all over.
Cut in half and serve warm.