Line a large baking pan with aluminum foil and place a wire rack on top. (I used a broiler pan and it worked out fine)
In a shallow microwavable dish whisk together the panko bread crumbs and olive oil; salt and pepper to taste. Microwave the crumbs, stirring constantly, until breadcrumbs are nicely browned. (watch this closely because microwave heats seem to vary a lot). After crumbs have cooled mix in the Parmesan cheese.
Place the flour in another shallow dish. In a medium-size bowl whisk together the eggs, thyme, and Dijon mustard.
Pat chops dry with paper toweling and generously salt and pepper them. Roll in flour, and then dip them into the egg mixture, and then in the bread crumbs pressing firmly to secure the breading onto the chops.
Place the chops on one side of the baking sheet.
Cut squash lengthwise into quarters and remove the seeds. Place on a microwavable plate and brush with 1 tablespoon of the melted butter. Microwave squash for 8-10 minutes or until softened. Place squash on the other half of the baking sheet. Mix the brown sugar with the remaining butter, mix in the cayenne pepper, and brush it over the squash.
Bake until chops are 145F and squash is golden brown and tender. (about 25 min depending on thickness)