Heat the 12-inch skillet over medium-high heat and add 2 tablespoons olive oil.
Add the potato pieces and cook, undisturbed when possible, about 7 minutes until a golden crust forms.
Add the chopped red onion, minced garlic, and 1 teaspoon oregano; continue cooking about 7 minutes more until potatoes are fork-tender.
Season the potatoes with salt and pepper to taste and remove from heat; stir in a little chopped parsley if desired.
In a large bowl, crumble the extra-firm tofu with your hands until it resembles coarse crumbs.
Add veganaise, 1 tablespoon yellow mustard, 1/4 teaspoon cayenne, 1 teaspoon turmeric, 2 tablespoons chopped parsley, 1 tablespoon chopped dill, 2 tablespoons chopped cilantro, chopped green onions, chopped cherry tomatoes, lime juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper to the tofu and mix well.
Taste the tofu mixture and adjust salt, pepper, or veganaise for creaminess as desired.
To assemble, place a spinach tortilla on a work surface; top with about 1/2 cup cooked potatoes, 1/2 cup tofu salad, and a sprinkle of shredded vegan cheddar, then roll up tightly and wrap in foil.
Repeat with remaining tortillas and fillings.
