Heat a non-stick pan over medium heat. Once hot, add the half of the oil and all of the onion, saute until it browns and starts to soften. Then add the mushrooms and saute until browned and softened. Add more oil as needed.
Crumble in the sausage and brown while breaking up into smaller pieces until no longer pink. Next, add in the eggs. Move the eggs around the pan using a spatula until they are firm and no longer runny but still moist. Then remove from the heat. Adjust the seasoning with salt and pepper to taste.
Place the cheese on the wrap, add the jalapeno (if using) and then the eggs. Fold in the ends and roll tightly.
Heat a nonstick pan over medium heat, place the wrap seam side down until golden brown, then flip over and do the same on the other side.