Rinse the quinoa under cold water. Combine the quinoa and water in a saucepan. Bring to a boil, once boiling, reduce heat to a simmer and cook for about 15 minutes, or until the quinoa is tender and has absorbed all the water. Remove from heat and let it cool.
Prepare the pesto: combine the fresh basil, raw cashews, olive oil, nutritional yeast, garlic, salt, lime juice, and maple syrup in a blender. Blend on high-speed for 20-30 seconds. Transfer half of the pesto to the quinoa and stir to combine.
Prepare the mushrooms: Heat a teaspoon of oil in a non-stick skillet. Once hot, add the sliced mushrooms and cook for 4-5 minutes, or until tender. Deglaze with the soy sauce, stir, and cook for one more minute. Remove from heat and set aside.
Prepare the onions (optional): Heat about 1/3 cup of oil in a small saucepan. Once hot, add the sliced onions and fry for 3-4 minutes, or until golden brown. Remove from the oil and transfer to a plate lined with kitchen paper towel to remove excess oil.
To assemble: spread about 1 tbsp of pesto in the middle of a tortilla wrap. Add a few slices of mushrooms, about 1/4 cup of pesto quinoa, a couple slices of avocado, some shredded red cabbage, and 1-2 tbsp of fried onions.
Fold up the bottom over the filling, then fold the edges and roll it up tightly into a burrito shape. Repeat with the remaining tortillas and filling.
Enjoy at room temperature, or chilled! These wraps will keep for up to two days in the refrigerator.