Heat a nonstick skillet over medium-low heat. Coat lightly with cooking spray. Whisk eggs with salt, then cook slowly, stirring, until softly set, 5 to 6 minutes.

Divide avocado, eggs, and hash browns between tortillas. Roll tightly into burritos, folding in sides. Set seam-side down.

Heat skillet over medium heat. Add jalapeño slices in two lines and cook until softened, about 2 minutes.

Sprinkle mozzarella over jalapeños. Increase heat to medium-high and cook until melted and lightly browned, 1 to 2 minutes.

Place burritos seam-side down onto cheese. Press gently to adhere, then flip and cook until crisp on both sides, about 2 minutes per side.

Serve immediately with salsa, sour cream, or Greek yogurt.