Peel the butternut squash and cut into uniform baton-cut wedges.
Place cornstarch in a large bowl.
Add squash pieces and toss until evenly coated in cornstarch.
Beat the egg in a separate bowl to make an egg wash.
Dip each coated squash piece into the egg wash.
Season the coated pieces with salt, black pepper, garlic powder, and paprika.
Preheat the air fryer to 400°F for 3 minutes.
Arrange fries in a single layer on the air fryer’s wire rack insert, leaving space between pieces.
Mist lightly with cooking spray.
Cook for 15 minutes without opening the basket.
Flip each piece with tongs.
Cook an additional 8–10 minutes until golden brown and crisp.
While fries cook, mix the mayonnaise, lemon juice, minced garlic, thyme, onion powder, smoked paprika, and a pinch of salt and pepper to make the chipotle-style aioli.
Serve the fries immediately with the chipotle aioli for dipping.