Peel and trim potatoes. Run through a spiralizer using the thinnest noodle blade, or cut into very thin matchsticks with a sharp steak knife.
Soak strands in cold water for 10 minutes. Drain and pat completely dry with a kitchen towel.
Wrap small handfuls of strands tightly around 2 skewers or a fork to form egg-sized nests.
Heat 2 inches of avocado oil to 300°F (150°C). Fry nests in batches of 2 to 3 for 3 to 4 minutes until pale and set. Drain on paper towels and rest.
Whisk together vegan mayo, chopped chipotle peppers, adobo sauce, smoked paprika, garlic powder, onion powder, salt, and pepper. Taste and add more seasoning if desired.
Increase oil to 375°F (190°C). Refry nests in batches for 2 to 3 minutes until deep golden and crisp.
Drain, salt immediately, top with vegan parmesan and parsley, and serve hot with chipotle mayo.
Notes
Soaking and drying the potatoes is essential for crispiness. The double fry is non-negotiable for that shatter-crisp texture.