Using a sharp knife, make a dotted line lengthwise around the entire squash. Place whole squash in the microwave and cook on full power for 5 minutes. Transfer to a cutting board and cut the squash in half using the dotted line as a guide. Wrap one half in plastic wrap and refrigerate for another use.
Spoon pulp and seeds out of remaining half and discard. Brush olive oil over all of the flesh and sprinkle with salt and pepper.
Preheat an air fryer to 360 degrees F (180 degrees C).
Place spaghetti squash half skin side-down in the air fryer basket. Cook for 20 minutes.
Transfer to a cutting board and fluff with a fork to resemble noodles. Finely chop noodles and place in a bowl. Add bread crumbs and Parmesan cheese. Mix well and form into tots.
Increase the temperature of the air fryer to 400 degrees F (200 degrees C).
Place tots in the air fryer basket and spray the tops with nonstick cooking spray. Cook for 5 minutes. Shake and cook until desired crispness, about 5 minutes more.