Heat 1 tablespoon oil in a medium nonstick skillet over medium heat. Add the scallion whites, half of the scallion greens (save the other half for garnish) and the jalapeno and cook, stirring, 1 to 2 minutes. Scrape half the vegetables into a small bowl and set aside; leave the remaining vegetables in the skillet.
Meanwhile, in a medium bowl, whisk together the eggs, rice flour, cilantro and water. Season with salt and pepper. Pour half the egg mixture over the vegetables in the skillet. Mix so everything is combined and cook over medium heat until the bottom is golden brown, 1 to 2 minutes. Flip and cook until the other side is golden brown. Turn the egg wrap out onto a cutting board. Repeat this with the remaining cooked vegetables and egg mixture.
In a medium bowl, combine 2 tablespoons oil, lemon juice and salt and pepper to taste. Whisk to combine, add the watercress and toss to coat evenly with the dressing.
To assemble, spoon half the goat cheese over each wrap and lay the watercress salad on top. Fold the wrap over the filling like a burrito, sprinkle with the reserved scallion greens, and enjoy hot.