Remove top and bottom ends from the squash. Remove seeds. Cut in half widthwise to make coring the seeds easier. Slice into ¼” thick rings.
Whisk eggs with salt and pepper in a medium bowl. Add squash rings and toss until well coated.
In a separate bowl, mix parmesan with cayenne and thyme. Drag the rings through the parmesan, leaving a mound of the cheese and spice mixture on each ring.
Place rings on a parchment-lined baking sheet. Bake at 400 degrees for 12 to 15 minutes or until desired crispness. The rings should be crispy when you bite into them.
May be stored for 24 hours, lightly covered with parchment. Use as an appetizer or salad garnish.